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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Origami Simulator</title>

    <link href="dependencies/bootstrap.min.css" rel="stylesheet" type="text/css"/>
    <link rel="stylesheet" type="text/css" href="dependencies/flat-ui.min.css"/>
    <link rel="stylesheet" type="text/css" href="dependencies/jquery-ui.min.css"/>
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    <link rel="stylesheet" type="text/css" href="css/nav.css"/>
    <link rel="stylesheet" type="text/css" href="css/main.css"/>

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    <script id="vertexShader" type="x-shader/x-vertex">
        attribute vec2 a_position;
        void main() {
           gl_Position = vec4(a_position, 0, 1);
        }
    </script>

    <script id="packToBytesShader" type="x-shader/x-fragment">
        precision mediump float;
        uniform vec2 u_floatTextureDim;
        uniform sampler2D u_floatTexture;
        uniform float u_vectorLength;
        float shift_right (float v, float amt) {
            v = floor(v) + 0.5;
            return floor(v / exp2(amt));
        }
        float shift_left (float v, float amt) {
            return floor(v * exp2(amt) + 0.5);
        }
        float mask_last (float v, float bits) {
            return mod(v, shift_left(1.0, bits));
        }
        float extract_bits (float num, float from, float to) {
            from = floor(from + 0.5); to = floor(to + 0.5);
            return mask_last(shift_right(num, from), to - from);
        }
        vec4 encode_float (float val) {
            if (val == 0.0) return vec4(0, 0, 0, 0);
            float sign = val > 0.0 ? 0.0 : 1.0;
            val = abs(val);
            float exponent = floor(log2(val));
            float biased_exponent = exponent + 127.0;
            float fraction = ((val / exp2(exponent)) - 1.0) * 8388608.0;
            float t = biased_exponent / 2.0;
            float last_bit_of_biased_exponent = fract(t) * 2.0;
            float remaining_bits_of_biased_exponent = floor(t);
            float byte4 = extract_bits(fraction, 0.0, 8.0) / 255.0;
            float byte3 = extract_bits(fraction, 8.0, 16.0) / 255.0;
            float byte2 = (last_bit_of_biased_exponent * 128.0 + extract_bits(fraction, 16.0, 23.0)) / 255.0;
            float byte1 = (sign * 128.0 + remaining_bits_of_biased_exponent) / 255.0;
            return vec4(byte4, byte3, byte2, byte1);
        }
        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            float textureXcoord = floor((fragCoord.x - 0.5)/u_vectorLength+0.0001) + 0.5;
            vec4 data = texture2D(u_floatTexture, vec2(textureXcoord, fragCoord.y)/u_floatTextureDim);
            int textureIndex = int(floor(mod(fragCoord.x-0.5+0.0001, u_vectorLength)));
            if (textureIndex == 0) gl_FragColor = encode_float(data[0]);
            else if (textureIndex == 1) gl_FragColor = encode_float(data[1]);
            else if (textureIndex == 2) gl_FragColor = encode_float(data[2]);
            else if (textureIndex == 3) gl_FragColor = encode_float(data[3]);
        }
    </script>

    <script id="zeroTexture" type="x-shader/x-fragment">
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        precision mediump float;
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        void main(){
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            gl_FragColor = vec4(0.0);
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        }
    </script>
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    <script id="zeroThetaTexture" type="x-shader/x-fragment">
        precision mediump float;
        uniform sampler2D u_theta;
        uniform vec2 u_textureDimCreases;
        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDimCreases;
            vec4 theta = texture2D(u_theta, scaledFragCoord);
            gl_FragColor = vec4(0.0, 0.0, theta[2], theta[3]);
        }
    </script>
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    <script id="centerTexture" type="x-shader/x-fragment">
        precision mediump float;
        uniform sampler2D u_lastPosition;
        uniform vec2 u_textureDim;
        uniform vec3 u_center;
        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDim;
            vec3 position = texture2D(u_lastPosition, scaledFragCoord).xyz;
            gl_FragColor = vec4(position-u_center, 0.0);
        }
    </script>
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    <script id="positionCalcShader" type="x-shader/x-fragment">
        precision mediump float;
        uniform vec2 u_textureDim;
        uniform float u_dt;
        uniform sampler2D u_lastPosition;
        uniform sampler2D u_velocity;
        uniform sampler2D u_mass;

        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDim;

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            vec3 lastPosition = texture2D(u_lastPosition, scaledFragCoord).xyz;

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            float isFixed = texture2D(u_mass, scaledFragCoord).y;
            if (isFixed == 1.0){
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                gl_FragColor = vec4(lastPosition, 0.0);
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                return;
            }

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            vec4 velocityData = texture2D(u_velocity, scaledFragCoord);
            vec3 position = velocityData.xyz*u_dt + lastPosition;
            gl_FragColor = vec4(position, velocityData.a);//velocity.a has error info
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        }
    </script>

    <script id="velocityCalcShader" type="x-shader/x-fragment">
        precision mediump float;
        uniform vec2 u_textureDim;
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        uniform vec2 u_textureDimEdges;
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        uniform vec2 u_textureDimFaces;
        uniform vec2 u_textureDimCreases;
        uniform vec2 u_textureDimNodeCreases;
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        uniform float u_creasePercent;
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        uniform float u_dt;
        uniform sampler2D u_lastPosition;
        uniform sampler2D u_lastVelocity;
        uniform sampler2D u_originalPosition;
        uniform sampler2D u_externalForces;
        uniform sampler2D u_mass;
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        uniform sampler2D u_meta;//[beamsIndex, numBeam, nodeCreaseMetaIndex, numCreases]
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        uniform sampler2D u_beamMeta;//[k, d, length, otherNodeIndex]
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        uniform sampler2D u_creaseMeta;//[k, d, targetTheta]
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        uniform sampler2D u_nodeCreaseMeta;//[creaseIndex, nodeIndex, -, -]
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        uniform sampler2D u_normals;
        uniform sampler2D u_theta;//[theta, z, normal1Index, normal2Index]
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        uniform sampler2D u_creaseGeo;//[h1, h2, coef1, coef2]
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        uniform sampler2D u_meta2;//[nodesFaceIndex, numFaces]
        uniform sampler2D u_nodeFaceMeta;//[faceIndex, a, b, c]
        uniform sampler2D u_nominalTriangles;//[angleA, angleB, angleC]
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        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDim;

            vec2 mass = texture2D(u_mass, scaledFragCoord).xy;
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            if (mass[1] == 1.0){//fixed
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                gl_FragColor = vec4(0.0);
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                return;
            }
            vec3 force = texture2D(u_externalForces, scaledFragCoord).xyz;
            vec3 lastPosition = texture2D(u_lastPosition, scaledFragCoord).xyz;
            vec3 lastVelocity = texture2D(u_lastVelocity, scaledFragCoord).xyz;
            vec3 originalPosition = texture2D(u_originalPosition, scaledFragCoord).xyz;

            vec4 neighborIndices = texture2D(u_meta, scaledFragCoord);
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            vec4 meta = texture2D(u_meta, scaledFragCoord);
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            float nodeError = 0.0;

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            for (int j=0;j<100;j++){//for all beams (up to 100, had to put a const int in here)
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                if (j >= int(meta[1])) break;

                float beamIndex1D = meta[0]+float(j);
                vec2 beamIndex = vec2(mod(beamIndex1D, u_textureDimEdges.x)+0.5, floor(beamIndex1D/u_textureDimEdges.x)+0.5);
                vec2 scaledBeamIndex = beamIndex/u_textureDimEdges;
                vec4 beamMeta = texture2D(u_beamMeta, scaledBeamIndex);

                float neighborIndex1D = beamMeta[3];
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                vec2 neighborIndex = vec2(mod(neighborIndex1D, u_textureDim.x)+0.5, floor(neighborIndex1D/u_textureDim.x)+0.5);
                vec2 scaledNeighborIndex = neighborIndex/u_textureDim;
                vec3 neighborLastPosition = texture2D(u_lastPosition, scaledNeighborIndex).xyz;
                vec3 neighborLastVelocity = texture2D(u_lastVelocity, scaledNeighborIndex).xyz;
                vec3 neighborOriginalPosition = texture2D(u_originalPosition, scaledNeighborIndex).xyz;

                vec3 nominalDist = neighborOriginalPosition-originalPosition;
                vec3 deltaP = neighborLastPosition-lastPosition+nominalDist;
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                float deltaPLength = length(deltaP);
                deltaP -= deltaP*(beamMeta[2]/deltaPLength);
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                nodeError += abs(deltaPLength/length(nominalDist) - 1.0);
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                vec3 deltaV = neighborLastVelocity-lastVelocity;

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                vec3 _force = deltaP*beamMeta[0] + deltaV*beamMeta[1];
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                force += _force;
            }
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            nodeError /= meta[1];
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            for (int j=0;j<100;j++){//for all creases (up to 100, had to put a const int in here)
                if (j >= int(meta[3])) break;

                float nodeCreaseIndex1D = meta[2]+float(j);
                vec2 nodeCreaseIndex = vec2(mod(nodeCreaseIndex1D, u_textureDimNodeCreases.x)+0.5, floor(nodeCreaseIndex1D/u_textureDimNodeCreases.x)+0.5);
                vec2 scaledNodeCreaseIndex = nodeCreaseIndex/u_textureDimNodeCreases;
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                vec4 nodeCreaseMeta = texture2D(u_nodeCreaseMeta, scaledNodeCreaseIndex);//[creaseIndex, length to node, nodeType (1 or 2), isReaction]
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                float creaseIndex1D = nodeCreaseMeta[0];
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                vec2 creaseIndex = vec2(mod(creaseIndex1D, u_textureDimCreases.x)+0.5, floor(creaseIndex1D/u_textureDimCreases.x)+0.5);
                vec2 scaledCreaseIndex = creaseIndex/u_textureDimCreases;

                vec4 thetas = texture2D(u_theta, scaledCreaseIndex);
                vec3 creaseMeta = texture2D(u_creaseMeta, scaledCreaseIndex).xyz;//[k, d, targetTheta]
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                vec4 creaseGeo = texture2D(u_creaseGeo, scaledCreaseIndex);//[h1, h2, coef1, coef2]
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                if (creaseGeo[0]< 0.0) continue;//crease disabled bc it has collapsed too much
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                float targetTheta = creaseMeta[2] * u_creasePercent;
                float angForce = creaseMeta[0]*(targetTheta-thetas[0]);// + creaseMeta[1]*thetas[1];

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                float nodeNum = nodeCreaseMeta[1];//1, 2, 3, 4
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                if (nodeNum > 2.0){//crease reaction, node is on a crease
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                    //node #1
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                    float normalIndex1D = thetas[2];
                    vec2 normalsIndex = vec2(mod(normalIndex1D, u_textureDimFaces.x)+0.5, floor(normalIndex1D/u_textureDimFaces.x)+0.5);
                    vec2 scaledNormalsIndex = normalsIndex/u_textureDimFaces;
                    vec3 normal1 = texture2D(u_normals, scaledNormalsIndex).xyz;

                    //node #2
                    normalIndex1D = thetas[3];
                    normalsIndex = vec2(mod(normalIndex1D, u_textureDimFaces.x)+0.5, floor(normalIndex1D/u_textureDimFaces.x)+0.5);
                    scaledNormalsIndex = normalsIndex/u_textureDimFaces;
                    vec3 normal2 = texture2D(u_normals, scaledNormalsIndex).xyz;

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                    float coef1 = creaseGeo[2];
                    float coef2 = creaseGeo[3];
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                    if (nodeNum == 3.0){
                        coef1 = 1.0-coef1;
                        coef2 = 1.0-coef2;
                    }
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                    vec3 _force = -angForce*(coef1/creaseGeo[0]*normal1 + coef2/creaseGeo[1]*normal2);
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                    force += _force;
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                } else {
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                    float normalIndex1D = thetas[2];//node #1
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                    float momentArm = creaseGeo[0];//node #1
                    if (nodeNum == 2.0) {
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                        normalIndex1D = thetas[3];//node #2
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                        momentArm = creaseGeo[1];//node #2
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                    }
                    vec2 normalsIndex = vec2(mod(normalIndex1D, u_textureDimFaces.x)+0.5, floor(normalIndex1D/u_textureDimFaces.x)+0.5);
                    vec2 scaledNormalsIndex = normalsIndex/u_textureDimFaces;
                    vec3 normal = texture2D(u_normals, scaledNormalsIndex).xyz;

                    vec3 _force = angForce/momentArm*normal;
                    force += _force;
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                }
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            }

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            vec3 velocity = force*u_dt/mass[0] + lastVelocity;
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            gl_FragColor = vec4(velocity,nodeError);
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        }
    </script>

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    <script id="thetaCalcShader" type="x-shader/x-fragment">
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        #define TWO_PI 6.283185307179586476925286766559
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        precision mediump float;
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        uniform vec2 u_textureDim;
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        uniform vec2 u_textureDimFaces;
        uniform vec2 u_textureDimCreases;
        uniform sampler2D u_normals;
        uniform sampler2D u_lastTheta;
        uniform sampler2D u_creaseVectors;
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        uniform sampler2D u_lastPosition;
        uniform sampler2D u_originalPosition;
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        uniform float u_dt;
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        void main(){

            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDimCreases;

            vec4 lastTheta = texture2D(u_lastTheta, scaledFragCoord);

            if (lastTheta[2]<0.0){
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                gl_FragColor = vec4(lastTheta[0], 0.0, -1.0, -1.0);
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                return;
            }

            vec2 normal1Index = vec2(mod(lastTheta[2], u_textureDimFaces.x)+0.5, floor(lastTheta[2]/u_textureDimFaces.x)+0.5);
            normal1Index /= u_textureDimFaces;
            vec2 normal2Index = vec2(mod(lastTheta[3], u_textureDimFaces.x)+0.5, floor(lastTheta[3]/u_textureDimFaces.x)+0.5);
            normal2Index /= u_textureDimFaces;

            vec3 normal1 = texture2D(u_normals, normal1Index).xyz;
            vec3 normal2 = texture2D(u_normals, normal2Index).xyz;

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            float dotNormals = dot(normal1, normal2);//normals are already normalized, no need to divide by length
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            if (dotNormals < -1.0) dotNormals = -1.0;
            else if (dotNormals > 1.0) dotNormals = 1.0;
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            vec2 creaseVectorIndices = texture2D(u_creaseVectors, scaledFragCoord).xy;
            vec2 creaseNodeIndex = vec2(mod(creaseVectorIndices[0], u_textureDim.x)+0.5, floor(creaseVectorIndices[0]/u_textureDim.x)+0.5);
            vec2 scaledNodeIndex = creaseNodeIndex/u_textureDim;
            vec3 node0 = texture2D(u_lastPosition, scaledNodeIndex).xyz + texture2D(u_originalPosition, scaledNodeIndex).xyz;
            creaseNodeIndex = vec2(mod(creaseVectorIndices[1], u_textureDim.x)+0.5, floor(creaseVectorIndices[1]/u_textureDim.x)+0.5);
            scaledNodeIndex = creaseNodeIndex/u_textureDim;
            vec3 node1 = texture2D(u_lastPosition, scaledNodeIndex).xyz + texture2D(u_originalPosition, scaledNodeIndex).xyz;

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            //https://math.stackexchange.com/questions/47059/how-do-i-calculate-a-dihedral-angle-given-cartesian-coordinates
            vec3 creaseVector = normalize(node1-node0);
            float x = dotNormals;
            float y = dot(cross(normal1, creaseVector), normal2);
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            float theta = atan(y, x);

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            float diff = theta-lastTheta[0];
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            float origDiff = diff;
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            if (diff < -5.0) {
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                diff += TWO_PI;
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            } else if (diff > 5.0) {
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                diff -= TWO_PI;
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            }
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            theta = lastTheta[0] + diff;
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            gl_FragColor = vec4(theta, diff, lastTheta[2], lastTheta[3]);//[theta, w, normal1Index, normal2Index]
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        }
    </script>
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    <script id="normalCalc" type="x-shader/x-fragment">
        precision mediump float;
        uniform vec2 u_textureDim;
        uniform vec2 u_textureDimFaces;
        uniform sampler2D u_faceVertexIndices;
        uniform sampler2D u_lastPosition;
        uniform sampler2D u_originalPosition;

        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDimFaces;

            vec3 indices = texture2D(u_faceVertexIndices, scaledFragCoord).xyz;

            float nodeIndex1D = indices[0];
            vec2 nodeIndex = vec2(mod(nodeIndex1D, u_textureDim.x)+0.5, floor(nodeIndex1D/u_textureDim.x)+0.5);
            vec2 scaledNodeIndex = nodeIndex/u_textureDim;
            vec3 a = texture2D(u_lastPosition, scaledNodeIndex).xyz + texture2D(u_originalPosition, scaledNodeIndex).xyz;

            nodeIndex1D = indices[1];
            nodeIndex = vec2(mod(nodeIndex1D, u_textureDim.x)+0.5, floor(nodeIndex1D/u_textureDim.x)+0.5);
            scaledNodeIndex = nodeIndex/u_textureDim;
            vec3 b = texture2D(u_lastPosition, scaledNodeIndex).xyz + texture2D(u_originalPosition, scaledNodeIndex).xyz;

            nodeIndex1D = indices[2];
            nodeIndex = vec2(mod(nodeIndex1D, u_textureDim.x)+0.5, floor(nodeIndex1D/u_textureDim.x)+0.5);
            scaledNodeIndex = nodeIndex/u_textureDim;
            vec3 c = texture2D(u_lastPosition, scaledNodeIndex).xyz + texture2D(u_originalPosition, scaledNodeIndex).xyz;

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            vec3 normal = normalize(cross(b-a, c-a));

            gl_FragColor = vec4(normal, 0.0);
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        }
    </script>
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    <script id="updateCreaseGeo" type="x-shader/x-fragment">
        precision mediump float;
        uniform vec2 u_textureDim;
        uniform vec2 u_textureDimCreases;
        uniform sampler2D u_lastPosition;
        uniform sampler2D u_originalPosition;
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        uniform sampler2D u_creaseMeta2;
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        void main(){
            vec2 fragCoord = gl_FragCoord.xy;
            vec2 scaledFragCoord = fragCoord/u_textureDimCreases;

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            vec4 creaseMeta = texture2D(u_creaseMeta2, scaledFragCoord);
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            vec2 node1Index = vec2(mod(creaseMeta[0], u_textureDim.x)+0.5, floor(creaseMeta[0]/u_textureDim.x)+0.5)/u_textureDim;
            vec2 node2Index = vec2(mod(creaseMeta[1], u_textureDim.x)+0.5, floor(creaseMeta[1]/u_textureDim.x)+0.5)/u_textureDim;
            vec2 node3Index = vec2(mod(creaseMeta[2], u_textureDim.x)+0.5, floor(creaseMeta[2]/u_textureDim.x)+0.5)/u_textureDim;
            vec2 node4Index = vec2(mod(creaseMeta[3], u_textureDim.x)+0.5, floor(creaseMeta[3]/u_textureDim.x)+0.5)/u_textureDim;

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            vec3 node1 = texture2D(u_originalPosition, node1Index).xyz + texture2D(u_lastPosition, node1Index).xyz;
            vec3 node2 = texture2D(u_originalPosition, node2Index).xyz + texture2D(u_lastPosition, node2Index).xyz;
            vec3 node3 = texture2D(u_originalPosition, node3Index).xyz + texture2D(u_lastPosition, node3Index).xyz;
            vec3 node4 = texture2D(u_originalPosition, node4Index).xyz + texture2D(u_lastPosition, node4Index).xyz;
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            float tol = 0.01;
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            vec3 creaseVector = node4-node3;
            float creaseLength = length(creaseVector);
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            if (abs(creaseLength)<tol) {
                gl_FragColor = vec4(-1);//disable crease
                return;
            }
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            creaseVector /= creaseLength;

            vec3 vector1 = node1-node3;
            vec3 vector2 = node2-node3;

            float proj1Length = dot(creaseVector, vector1);
            float proj2Length = dot(creaseVector, vector2);
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            float dist1 = sqrt(abs(vector1.x*vector1.x+vector1.y*vector1.y+vector1.z*vector1.z-proj1Length*proj1Length));
            float dist2 = sqrt(abs(vector2.x*vector2.x+vector2.y*vector2.y+vector2.z*vector2.z-proj2Length*proj2Length));

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            if (dist1<tol || dist2<tol){
                gl_FragColor = vec4(-1);//disable crease
                return;
            }
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            gl_FragColor = vec4(dist1, dist2, proj1Length/creaseLength, proj2Length/creaseLength);
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        }
    </script>

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    <script type="text/javascript" src="dependencies/jquery-3.1.1.min.js"></script>
    <script type="text/javascript" src="dependencies/jquery-ui.min.js"></script>
    <script type="text/javascript" src="dependencies/flat-ui.min.js"></script>
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    <script type="text/javascript" src="dependencies/three.js"></script>
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    <script type="text/javascript" src="dependencies/binary_stl_writer.js"></script>
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    <script type="text/javascript" src="dependencies/TrackballControls.js"></script>
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    <script type="text/javascript" src="dependencies/Projector.js"></script>
    <script type="text/javascript" src="dependencies/SVGRenderer.js"></script>
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    <script type="text/javascript" src="dependencies/underscore-min.js"></script>
    <script type="text/javascript" src="dependencies/FileSaver.min.js"></script>
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    <script type="text/javascript" src="dependencies/SVGLoader.js"></script>
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    <script type="text/javascript" src="dependencies/OBJExporter.js"></script>
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    <script type="text/javascript" src="dependencies/path-data-polyfill.js"></script>
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    <script type="text/javascript" src="dependencies/earcut.js"></script>
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    <script type="text/javascript" src="dependencies/numeric-1.2.6.js"></script>
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    <script type="text/javascript" src="dependencies/EffectComposer.js"></script>
    <script type="text/javascript" src="dependencies/MaskPass.js"></script>
    <script type="text/javascript" src="dependencies/ShaderPass.js"></script>
    <script type="text/javascript" src="dependencies/CopyShader.js"></script>
    <script type="text/javascript" src="dependencies/SSAOShader.js"></script>
    <script type="text/javascript" src="dependencies/Detector.js"></script>
    <script type="text/javascript" src="dependencies/RenderPass.js"></script>

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    <script type="text/javascript" src="dependencies/WebVR.js"></script>
    <script type="text/javascript" src="dependencies/VREffect.js"></script>
    <script type="text/javascript" src="dependencies/ViveController.js"></script>
    <script type="text/javascript" src="dependencies/VRControls.js"></script>

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    <script type="text/javascript" src="js/dynamic/GLBoilerplate.js"></script>
    <script type="text/javascript" src="js/dynamic/GPUMath.js"></script>
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    <script type="text/javascript" src="js/controls.js"></script>
    <script type="text/javascript" src="js/threeView.js"></script>
    <script type="text/javascript" src="js/globals.js"></script>
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    <script type="text/javascript" src="js/node.js"></script>
    <script type="text/javascript" src="js/beam.js"></script>
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    <script type="text/javascript" src="js/crease.js"></script>
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    <script type="text/javascript" src="js/model.js"></script>
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    <script type="text/javascript" src="js/3dUI.js"></script>
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    <script type="text/javascript" src="js/staticSolver.js"></script>
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    <script type="text/javascript" src="js/dynamic/dynamicSolver.js"></script>
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    <script type="text/javascript" src="js/rigidSolver.js"></script>
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    <script type="text/javascript" src="js/pattern.js"></script>
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    <script type="text/javascript" src="js/saveSTL.js"></script>
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    <script type="text/javascript" src="js/saveFOLD.js"></script>
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    <script type="text/javascript" src="js/importer.js"></script>
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    <script type="text/javascript" src="js/ViveInterface.js"></script>
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    <script type="text/javascript" src="js/main.js"></script>
</head>
<body>
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<nav id="globalNav" class="navbar navbar-inverse navbar-embossed" role="navigation">
    <div class="navbar-header">
        <a id="logo" class="navbar-brand" target="_blank" href="http://cba.mit.edu/">
            <img id="inactiveLogo" src="logo.png"/>
            <img id="activeLogo" src="logo-active.png"/>
        </a>
    </div>
    <div class="collapse navbar-collapse" id="navbar-collapse-01">
        <ul class="nav navbar-nav navbar-left">
            <li class="dropdown navDropdown">
                <a href="#" class="dropdown-toggle" data-toggle="dropdown">File <b class="caret"></b></a>
                <span class="dropdown-arrow"></span>
                <ul class="dropdown-menu">
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                    <li><a class="loadFile" href="#">Import... (SVG / FOLD)</a></li>
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                    <li><a id="tips" href="#">File Import Tips</a></li>
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                    <li class="divider"></li>
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                    <li><a id="exportFOLD" href="#">Save Simulation as FOLD...</a></li>
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                    <li><a id="exportSTL" href="#">Save Simulation as STL...</a></li>
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                    <li><a id="exportOBJ" href="#">Save Simulation as OBJ...</a></li>
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                    <li class="divider"></li>
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                    <li><a id="saveSVG" href="#">Save Pattern as SVG...</a></li>
                    <!--<li><a id="saveSVGScreenshot" href="#">Save SVG screenshot</a></li>-->
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                </ul>
            </li>
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            <li class="dropdown navDropdown">
                <a href="#" class="dropdown-toggle" data-toggle="dropdown">Examples <b class="caret"></b></a>
                <span class="dropdown-arrow"></span>
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                <ul class="dropdown-menu" style="min-width: 200px;">
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                    <li class="dropdown-submenu">
                        <a tabindex="-1">Origami<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo" data-url="Origami/randlettflappingbird.svg">Randlett Flapping Bird</a></li>
                            <li><a href="#" class="demo" data-url="Origami/singlesquaretwist.svg">Square Twist (single)</a></li>
                            <li><a href="#" class="demo" data-url="Origami/squaretwistManyAngles.svg">Square Twist (many angles)</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Tesselations<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo" data-url="Tessellations/miura-ori.svg">Miura-Ori</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/waterbomb.svg">Waterbomb (six-crease base)</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/waterbombTwist.svg">Waterbomb (eight-crease base)</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/reschtritessellation.svg">Resch Triangle Tessellation</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/reschbarbell.svg">Resch Barbell Tessellation</a></li>
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                            <li><a href="#" class="demo" data-url="Tessellations/honeycomb_333_cp.svg">Lang Honeycomb Tessellation</a></li>
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                            <li><a href="#" class="demo" data-url="Tessellations/oval_tessellation_cp.svg">Lang Oval Tessellation</a></li>
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                            <li><a href="#" class="demo" data-url="Tessellations/hyperbolic_limit_cp.svg">Lang Hyperbolic Limit</a></li>
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                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Curved Creases<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
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                            <li><a href="#" class="demo" data-url="Curved/huffmanTower.svg">Huffman Tower</a></li>
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                        </ul>
                    </li>
                    <li class="divider"></li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Problematic Patterns<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo" data-url="Origami/hypar.svg">Hypar</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/wedged_double_faced.svg">Lang Wedged Double Faced Tessellation</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/rattanweaveLang.svg">Lang Rattan Weave</a></li>
                        </ul>
                    </li>
                </ul>
            </li>
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            <li class="dropdown navDropdown">
                <a href="#" class="dropdown-toggle" data-toggle="dropdown">View <b class="caret"></b></a>
                <span class="dropdown-arrow"></span>
                <ul class="dropdown-menu">
                    <li><a id="menuVis" href="#">Toggle Menu Visibility</a></li>
                </ul>
            </li>
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            <li><a id="navPattern" href="#">Pattern</a></li>
            <li><a id="navSimulation" href="#">Simulation</a></li>
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            <li><a id="about" class="menuHoverControls" target="_blank" href="#">About</a></li>
        </ul>
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        <!--<form class="navbar-form navbar-right" action="#" role="search">-->
            <!--<div class="form-group">-->
              <!--<div class="input-group">-->
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                <div class="sliderInput floatRight" id="creasePercentNav">
                    <span class="label-slider">Fold Angle : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
                    <!--<input value="" placeholder="" class="form-control" type="text">-->
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                </div>
              <!--</div>-->
            <!--</div>-->
        <!--</form>-->
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    </div><!-- /.navbar-collapse -->
    <input id="fileSelector" type="file">

</nav>

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<div  id="threeContainer"></div>
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<canvas id="gpuMathCanvas"></canvas>
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<div id="controls">
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    <div class="sliderInput floatRight" id="creasePercent">
        <span class="label-slider">Fold Angle (-1 to 1) : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
        <input value="" placeholder="" class="form-control" type="text">
    </div><br/><br/>
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    <div id="simButtons" class="alignRight">
        <a href="#" id="start" class="paddingBottom btn btn-lg btn-success">Start Simulation</a>
        <a href="#" id="pause" class="paddingBottom btn btn-lg btn-warning">Pause Simulation</a>
        <a href="#" id="reset" class="paddingBottom btn btn-lg btn-default">Reset</a>
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        <div id="stepForwardOptions" class="floatRight">
            <a href="#" id="stepForward" class="btn btn-lg btn-default">Step Forward</a>
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            <label>Num Steps:</label> &nbsp;&nbsp;<input id="numSteps" value="100" placeholder="" class="form-control" type="text">
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            <br/><br/>
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        </div>
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    </div>
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    <!--<b>Simulation Type:</b><br/>-->
    <!--<div class="indent">-->
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        <!--<label class="radio">-->
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            <!--<input name="simType" value="dynamic" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>-->
            <!--Compliant Dynamic Simulation <a class="about floatRight" href="#" id="aboutDynamicSim"><span class="fui-question-circle"></span></a>-->
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        <!--</label>-->
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        <!--&lt;!&ndash;<label class="radio">&ndash;&gt;-->
            <!--&lt;!&ndash;<input name="simType" value="static" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>&ndash;&gt;-->
            <!--&lt;!&ndash;Compliant Static Simulation <a class="about floatRight" href="#" id="aboutStaticSim"><span class="fui-question-circle"></span></a>&ndash;&gt;-->
        <!--&lt;!&ndash;</label>&ndash;&gt;-->
        <!--&lt;!&ndash;<label class="radio">&ndash;&gt;-->
            <!--&lt;!&ndash;<input name="simType" value="rigid" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>&ndash;&gt;-->
            <!--&lt;!&ndash;Rigid Static Simulation <a class="about floatRight" href="#" id="aboutRigidSim"><span class="fui-question-circle"></span></a>&ndash;&gt;-->
        <!--&lt;!&ndash;</label>&ndash;&gt;-->
    <!--</div><br/>-->
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    <div class="inlineBlock fullWidth">
        <label class="checkbox floatRight" for="userInteractionEnabled">
            <input id="userInteractionEnabled" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
            Allow User Interaction
        </label>
    </div><br/>
    <div class="fullWidth alignRight">
        <a href="#" id="shouldCenterGeo" class="displayBlock btn btn-lg btn-default">Re-center geometry</a>
    </div><br/>
    <div class="fullWidth">
        <a href="#" class="seeMore closed" data-id="simulationSettings"><span class="fui-triangle-down"></span><b>Simulation Settings:</b></a><a class="about" href="#" id="aboutStiffness"><span class="fui-question-circle"></span></a><br/>
        <div id="simulationSettings" class="hide">
            <div class="sliderInput paddingBottom" id="axialStiffness">
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                <span class="label-slider">Axial Strength : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
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                <input value="" placeholder="" class="form-control" type="text">
            </div>
            <div class="sliderInput" id="creaseStiffness">
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                <span class="label-slider">Fold Strength : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
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                <input value="" placeholder="" class="form-control" type="text">
            </div>
            <div class="sliderInput" id="panelStiffness">
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                <span class="label-slider">Facet Strength : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
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                <input value="" placeholder="" class="form-control" type="text">
            </div>
            <div class="sliderInput" id="percentDamping">
                <span class="label-slider">Damping (0-1): </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
                <input value="" placeholder="" class="form-control" type="text">
            </div>
        </div><br/>
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    </div>
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    <div class="fullWidth">
        <a href="#" class="seeMore closed" data-id="animationsSettings"><span class="fui-triangle-down"></span><b>Animation Settings:</b></a><a class="about" href="#" id="aboutAnimation"><span class="fui-question-circle"></span></a><br/>
        <div id="animationsSettings" class="fullWidth hide">
            <div class="doubleIndent">
                <span class="smallTxt">&Delta;t = <span id="deltaT"></span> seconds</span><br/>
                <span class="smallTxt">Num simulation steps per render: &nbsp;&nbsp;<input id="numStepsPerRender" value="" placeholder="" class="int form-control" type="text"></span>
            </div>
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        </div>
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    </div><br/>
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    <div class="fullWidth">
        <a href="#" class="seeMore closed" data-id="errorInfo"><span class="fui-triangle-down"></span><b>Error:</b></a><a class="about" href="#" id="aboutError"><span class="fui-question-circle"></span></a><br/>
        <div id="errorInfo" class="hide smallTxt doubleIndent">
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            <label>Average vertex error: <span id="globalError"></span></label>
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        </div>
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    </div><br/>

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    <div class="extraSpace"></div>
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</div>
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<div id="svgViewer"></div>
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<div id="controlsLeft" class="flipped">
    <div>
        <b>View Settings:</b><br/><br/>
        <div class="indent">
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            <div>
                <a href="#" class="seeMore open" data-id="materialSettings"><span class="fui-triangle-down"></span>Mesh Material:</a>
            </div>
            <div id="materialSettings" class="inlineBlock indent">
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                <label class="checkbox" for="meshVisible">
                    <input id="meshVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Mesh Visible
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                </label>
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                <div id="meshMaterialOptions">
                    <label class="radio">
                        <input name="colorMode" value="color" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                        Colored Material
                    </label>
                    <div id="coloredMaterialOptions" class="indent">
                        <label>Color 1 (rgb hex): &nbsp;&nbsp;</label><input id="color1" value="" placeholder="" class="hexVal form-control" type="text"><br/>
                        <label>Color 2 (rgb hex): &nbsp;&nbsp;</label><input id="color2" value="" placeholder="" class="hexVal form-control" type="text"><br/>
                    </div>
                    <label class="radio">
                        <input name="colorMode" value="normal" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                        Face Normals Material
                    </label>
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                    <label class="radio">
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                        <input name="colorMode" value="axialStrain" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
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                        Strain Visualization<a class="about floatRight" href="#" id="aboutAxialStrain"><span class="fui-question-circle"></span></a>
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                    </label>
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                    <div id="axialStrainMaterialOptions" class="indent">
                        <label>Max Strain: &nbsp;&nbsp;</label>
                        <input id="strainClip" value="" placeholder="" class="float form-control" type="text"> %<br/>
                    </div>
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                </div>
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                <br/>
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            </div><br/>
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            <div>
                <a href="#" class="seeMore closed" data-id="edgeVisiblity"><span class="fui-triangle-down"></span>Edge Visiblity</a>:
            </div>
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            <div id="edgeVisiblity" class="hide indent">
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                <label class="checkbox" for="edgesVisible">
                    <input id="edgesVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Edges Visible
                </label>
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                <div id="edgeVisOptions" class="indent">
                    <label class="checkbox" for="mtnsVisible">
                        <input id="mtnsVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
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                        Mountains <span id="numMtns"></span>
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                    </label>
                    <label class="checkbox" for="valleysVisible">
                        <input id="valleysVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
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                        Valleys <span id="numValleys"></span>
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                    </label>
                    <label class="checkbox" for="panelsVisible">
                        <input id="panelsVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
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                        Facet Creases <span id="numFacets"></span>
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                    </label>
                    <label class="checkbox" for="passiveEdgesVisible">
                        <input id="passiveEdgesVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
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                        Undriven Edges <span id="numPassive"></span>
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                    </label>
                </div>
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                <br/>
            </div>
            <br/>
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            <!--Rendering:-->
            <!--<div class="indent">-->
                <!--<label class="checkbox" for="ambientOcclusion">-->
                    <!--<input id="ambientOcclusion" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>-->
                    <!--Ambient Occlusion-->
                <!--</label>-->
            <!--</div>-->
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            <div>
                <a href="#" class="seeMore closed" data-id="virtualReality"><span class="fui-triangle-down"></span>Virtual Reality:</a>
            </div>
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            <div id="virtualReality" class="hide indent smallTxt">
                Status: &nbsp;<span id="VRstatus"></span><a class="about floatRight" href="#" id="aboutVR"><span class="fui-question-circle"></span></a>
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                <div id="VRoptions"><br/>
                    <a href="#" id="enterVR" class="displayBlock btn btn-lg btn-inverse"></a>
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                </div><br/><br/>
            </div><br/>
            <div>
                <a href="#" class="seeMore closed" data-id="cameraAngle"><span class="fui-triangle-down"></span>View Angle:</a><br/>
            </div>
            <div id="cameraAngle" class="hide indent ">
                <a href="#" id="cameraZ" class="paddingBottom btn btn-sm btn-default">Front</a>
                <a href="#" id="cameraMinusZ" class="paddingBottom btn btn-sm btn-default">Back</a>
                <a href="#" id="cameraX" class="paddingBottom btn btn-sm btn-default">Right</a>
                <a href="#" id="cameraMinusX" class="paddingBottom btn btn-sm btn-default">Left</a><br/>
                <a href="#" id="cameraY" class="btn btn-sm btn-default">Top</a>
                <a href="#" id="cameraMinusY" class="btn btn-sm btn-default">Bottom</a>
                <a href="#" id="cameraOrtho" class="btn btn-sm btn-default">Ortho</a>
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            </div>
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            <div class="extraSpace"></div>
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        </div>
    </div>
</div>
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<div class="modal fade" id="aboutModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-body">
                <p><b>Origami Simulator</b><br/><br/>
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                    <a target="_blank" href="http://www2.eng.cam.ac.uk/~sdg/preprint/5OSME.pdf">Origami Folding; A Structural Engineering Approach</a><br/>
                    <a target="_blank" href="http://origami.c.u-tokyo.ac.jp/~tachi/cg/SimulationOfRigidOrigami_tachi_4OSME.pdf">Rigid Origami Simulator</a><br/>
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                    <br/>
                    This app uses <a target="_blank" href="https://threejs.org/">three.js</a> to visualize and interact with the 3D geometry of the folding.<br/>
                    Triangulation of quad faces in origami patterns is achieved by adding the shortest edge across the quad (this helps to preserve symmetry, which
                    makes the simulation work better). Arbitrary polygonal faces are triangulated using the <a target="_blank" href="https://github.com/mapbox/earcut">Earcut Library</a>.<br/>
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                    Additionally, I used <a target="_blank" href="https://jquery.com/">jQuery</a>, <a target="_blank" href="http://getbootstrap.com/">Bootstrap</a>, and the
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                    <a target="_blank" href="http://designmodo.github.io/Flat-UI/">Flat UI theme</a> to build the GUI.<br/>
                    <br/>
                    Built by <a href="http://www.amandaghassaei.com/" target="_blank">Amanda Ghassaei</a> as a final project for <a href="http://courses.csail.mit.edu/6.849/spring17/" target="_blank">Geometric Folding Algorithms</a>.
                    Code available on <a href="https://github.com/amandaghassaei/OrigamiSimulator" target="_blank">Github</a>.  If you have interesting crease patterns that would
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                    make good demo files, please send them to me (Amanda) so I can add them to the <b>Examples</b> menu.  My email address is on my website.  Thanks!
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                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="tipsModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-lg">
        <div class="modal-content">
            <div class="modal-body">
                <p><b>File Import Tips</b><br/><br/>
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                    Bad design files will throw errors and create models that explode or cannot be solved, here are some tips for
                    importing FOLD or svg files that work.<br/><br/>
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                    <b>Importing FOLD:</b><br/><br/>
                    The FOLD file format is specified in <a target="_blank" href="https://github.com/edemaine/fold">these docs</a>.
                    This tool imports FOLD v1.0 files with <b>all</b> of the following fields populated:
                    <ul>
                        <li>vertices_coords</li>
                        <li>edges_vertices</li>
                        <li>edges_assignment</li>
                        <li>faces_vertices</li>
                    </ul>
                    If you are unsure whether your FOLD file is valid, you can inspect it using the
                    <a target="_blank" href="https://edemaine.github.io/fold/examples/foldviewer.html">FOLD Viewer</a>.<br/>
                    <br/>
                    <b>Importing SVG:</b><br/><br/>
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                    <ul>
                        <li>The SVG importer supports path objects and line objects (coming).  Please convert polygons to paths before importing.</li>
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                        <li>Mountain folds are <span style="color:red">red</span> - rgb(255, 0, 0), hex #ff0000</li>
                        <li>Valley folds are <span style="color:blue">blue</span> - rgb(0, 0, 255), hex #0000ff</li>
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                        <li>Outline edges are <span style="color:black">black</span> - rgb(0, 0, 0), hex #000000</li>
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                    </ul>
                    <img src="assets/examplepattern.jpg"/>
                    <ul>
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                        <li>This tool will automatically triangulate regions in the pattern that form polygons with more than three sides.
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                        To control the triangulations draw lines in <span style="color:#cccc00">yellow</span> - rgb(255, 255, 0), hex #ffff00<br/>
                        In general, patterns move better when their triangulation is symmetric and minimizes long, skinny triangles.</li>
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                    </ul>
                    <img src="assets/patternwithtriangulations.jpg"/>
                    <ul>
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                        <li>Stroke and line style do not matter.</li>
                        <li>The final fold angle of a mountain or valley fold is set by its opacity. For example, 1.0 = 180&deg;
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                        (fully folded), 0.5 = 90&deg;, 0 = 0&deg; (flat).  Any fold angle between  0&deg; and 180&deg; may be used.</li>
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                        <li>This tool should be able to automatically clean files of slightly misaligned vertices, stray vertices,
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                        duplicate lines, and extra vertices falling in the middle of an edge,
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                        but it is recommended to remove these errors yourself in order to avoid problems.</li>
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                        <li>If your simulation is not working, check that the pattern looks correct by clicking on the "Pattern" view in the top nav bar.</li>
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                    </ul><br/>

                <b>For Adobe Illustrator users:</b><br/><br/>
                I use Illustrator to create SVGs (though any vector editing program should be fine), here are some tips I've found for making svgs to import into this tool.<br/><br/>
                    <ul>
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                        <li>If you are starting with a pre-made vector file, first ungroup any groups, release all compound paths
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                        (<b>Select all + Object>Compound Path>Release</b>), and release all clipping masks (<b>Select all + Object>Clipping Mask>Release</b>).</li>
                        <li>Create geometry using the <b>Line Segment Tool</b>.</li>
                        <li>Illustrator can help you select all lines of a particular type so that you can edit their color or opacity together.  Click the line,
                        then go to <b>Select>Same>Appearance</b> to select all similar lines in the pattern.
                        <li>To turn lines and polygons into path objects, select the geometry then right click and select <b>Make Compound Path</b>.</li>
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                        <li>Finally hit <b>Save As</b> and select <b>.svg</b> extension. I'm using the default SVG 1.1 settings, but version 1.0 will work as well.</li>
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                    </ul>
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                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="aboutVRmodal" tabindex="-1" role="dialog">
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    <div class="modal-dialog modal-lg">
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        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <p><b>VR</b><br/><br/>
                This tool currently supports an interactive Virtual Reality mode using the Vive headset and controllers.
                For this to work, you must first use a <a href="https://webvr.info/" target="_blank">WebVR enabled browser</a>:
                currently only <a href="https://webvr.rocks/firefox" target="_blank">Firefox Nightly</a> is supported by this app.
                <br/><br/>
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                When you open this page with the appropriate browser and a Vive connected through Steam VR, you will see a button that says "Enter VR".  Clicking this will
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                put the app in an interactive VR mode.  The hand controllers will allow you to grab the origami mesh and pull on it.
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                This is especially interesting if you set the <b>Mesh Material</b> to <b>Strain Visualization</b> so you can see how your interactions
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                change the internal strains in the material.
                <br/><br/>
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                If the simulation looks choppy, consider lowering the <b>Num simulation steps per render</b> setting under <b>Animation Settings</b> in the right hand menu.
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                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
<div class="modal fade" id="aboutAnimationModal" tabindex="-1" role="dialog">
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    <div class="modal-dialog modal-lg">
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        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <p><b>Animation Settings</b><br/><br/>
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                The dynamic simulation is calculated by solving for all the forces in the system, moving time forward in small <b>&Delta;t</b> steps,
                and updating the vertices of the origami incrementally.  The time step size for this animation is calculated automatically
                based on the material stiffnesses set in the <b>Simulation Settings</b> section: more stiff settings
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                require shorter time steps to solve and will slow down the simulation.<br/>
                <br/>
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                <b>Num simulation steps per render</b> allows you to control the number of tiny time steps forward to take on each
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                render cycle.  If the simulation looks choppy to you, you might consider lowering this setting.
                Lowering the number of steps per render will slow down the simulation, but will result in a more smooth animation.
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                </p>
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            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="exportSTLModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <b>Export STL</b><br/><br/>
                Filename: &nbsp;&nbsp;<input id="stlFilename" value="" placeholder="" class="bigInput text form-control" type="text"> .stl<br/><br/>
                Scale: &nbsp;&nbsp;<input value="" placeholder="" class="exportScale form-control" type="text"><br/><br/>
                Dimensions: &nbsp;&nbsp;<b><span class="exportDimensions"></span></b><br/>
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                <span class="smallTxt">(the STL file format is unitless, but typically assumed to be either in inches or mm)</span><br/>
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                <label class="bigLabel checkbox" for="doublesidedSTL">
                    <input id="doublesidedSTL" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Double Sided
                </label>
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            </div>
            <div class="modal-footer">
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                <button id="doSTLsave" type="button" class="actionButton btn btn-success" data-dismiss="modal">Save</button>
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            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
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<div class="modal fade" id="exportOBJModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
                <b>Export OBJ</b><br/><br/>
                Filename: &nbsp;&nbsp;<input id="objFilename" value="" placeholder="" class="bigInput text form-control" type="text"> .stl<br/><br/>
                Scale: &nbsp;&nbsp;<input value="" placeholder="" class="exportScale form-control" type="text"><br/><br/>
                Dimensions: &nbsp;&nbsp;<b><span class="exportDimensions"></span></b><br/>
                <span class="smallTxt">(the OBJ file format is unitless, but typically assumed to be either in inches or mm)</span><br/>
                <label class="bigLabel checkbox" for="doublesidedOBJ">
                    <input id="doublesidedOBJ" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Double Sided
                </label>
            </div>
            <div class="modal-footer">
                <button id="doOBJsave" type="button" class="actionButton btn btn-success" data-dismiss="modal">Save</button>
            </div>
        </div><!-- /.modal-content -->
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<div class="modal fade" id="exportFOLDModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <b>Export FOLD</b><br/><br/>
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                Filename: &nbsp;&nbsp;<input id="foldFilename" value="" placeholder="" class="bigInput text form-control" type="text"> .fold<br/><br/>
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                Author: &nbsp;&nbsp;<input id="foldAuthor" value="Amanda Ghassaei" placeholder="" class="bigInput text form-control" type="text"><br/><br/>
                Scale: &nbsp;&nbsp;<input value="" placeholder="" class="exportScale form-control" type="text">&nbsp;&nbsp;&nbsp;&nbsp;
                Units: &nbsp;&nbsp;
                <div class="btn-group">
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                    <button data-toggle="dropdown" class="btn btn-default dropdown-toggle" type="button"><span class="unitsDisplay"></span> <span class="caret"></span></button>
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                    <ul id="unitsDropdown" role="menu" class="dropdown-menu">
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                        <li><a class="units" data-id="unit" href="#">unitless</a></li>
                        <li><a class="units" data-id="in" href="#">in</a></li>
                        <li><a class="units" data-id="pt" href="#">pt</a></li>
                        <li><a class="units" data-id="m" href="#">m</a></li>
                        <li><a class="units" data-id="cm" href="#">cm</a></li>
                        <li><a class="units" data-id="mm" href="#">mm</a></li>
                        <li><a class="units" data-id="um" href="#">um</a></li>
                        <li><a class="units" data-id="nm" href="#">nm</a></li>
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                    </ul>
                </div>
                <br/><br/>
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                Dimensions: &nbsp;&nbsp;<b><span class="exportDimensions"></span> <span class="unitsDisplay"></span></b><br/>
                <label class="bigLabel checkbox" for="triangulateFOLDexport">
                    <input id="triangulateFOLDexport" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Save with triangulated faces
                </label>
                <label class="bigLabel checkbox" for="exportFoldAngle">
                    <input id="exportFoldAngle" data-toggle="checkbox" disabled class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Save with vertices_foldAngles (coming soon)
                </label>
                <span class="smallTxt">For more information about the FOLD file format, see the <a target="_blank" href="https://github.com/edemaine/fold">offical docs</a></span>.
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            </div>
            <div class="modal-footer">
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                <button id="doFOLDsave" type="button" class="actionButton btn btn-success" data-dismiss="modal">Save</button>
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            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="importFoldModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <b>Import FOLD</b><br/><br/>
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                <label class="bigLabel checkbox" for="foldUseAngles">
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                    <input id="foldUseAngles" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                    Use current angles as target fold angles
                </label>
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            </div>
            <div class="modal-footer">
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                <button data-dismiss="modal" type="button" class="btn btn-success">OK</button>
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            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
<div class="modal fade" id="warningModal" tabindex="-1" role="dialog">
    <div class="modal-dialog sm">
        <div class="modal-content">
            <div class="modal-body">
                <p id="warningMessage">
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="aboutErrorModal" tabindex="-1" role="dialog">
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    <div class="modal-dialog modal-lg">
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        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
                <p><b>Simulation Error</b><br/><br/>
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                    <b>Average vertex error</b> gives a sense of how much the distance constraints in the
                    origami pattern are being violated (i.e. how much the sheet is being stretched).  The error at each vertex is evaluated by averaging the
                    percent deviation of all its distance constraints with adjacent vertices.  This error is
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                    reported as a percent of the total length of the distance constraint to remove scaling effects.
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                    <br/><br/>
                    This measurement is equivalent to <a href="https://en.wikipedia.org/wiki/Deformation_(mechanics)#Engineering_strain" target="_blank">
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                        Cauchy strain or engineering strain</a> of the distance constraints on this system.
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                    Increasing the <b>Axial Stiffness</b> will tighten these constraints and
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                    lower the error in the simulation.<br/>
                    <br/>
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                    To visualize the error of each vertex graphically, select <b>Strain Visualization</b> under <b>Mesh Material</b>
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                     in the left menu.
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="aboutStiffnessModal" tabindex="-1" role="dialog">
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    <div class="modal-dialog modal-lg">
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        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <p><b>Simulation Settings</b><br/><br/>
                    This app uses a compliant dynamic simulation method to solve for the geometry of an origami pattern
                    at a given fold angle.  The simulation sets up several types of constraints: distance constraints prevent the
                    sheet from stretching or compressing, and angular constraints fold or flatten the sheet.  Each of these constraints is weighted by a stiffness - the stiffer the constraint, the better it is enforced
                    in the simulation.  <br/>
                    <br/>
                    <b>Axial Stiffness</b> is the stiffness of the distance constraints.  Increasing axial
                    stiffness will decrease the strain in the simulation, but it will also slow down the solver.  <br/>
                    <br/>
                    Fold and facet stiffnesses correspond to two types of angular constraints.  <b>Fold Stiffness</b> is the stiffness of the mountain
                    and valley creases in the origami pattern.  <b>Facet Stiffness</b> is the stiffness of the triangulated faces between
                    creases in the pattern.  Increasing facet stiffness causes the faces between creases to stay very flat as the origami is folded.
                    As facet stiffness becomes very high, this simulation approaches a <a href="http://www.tsg.ne.jp/TT/cg/TachiFreeformOrigami2010.pdf" target="_blank">
                        rigid origami simulation</a>, and models the behavior of a rigid material (such as metal) when folded.<br/>
                    <br/>
                    Constraints <i>strengths</i> (units of N) are scaled by the length of a particular constraint to determine the <i>stiffness</i>.  Axial stiffness is calculated by dividing
                    axial strength by length; angular stiffness is calculated by multiplying fold or facet strength by length.<br/>
                    <br/>
                    Since this is a dynamic simulation, vertices of the origami move with some notion of acceleration and velocity.  In order to
                    keep the system stable and help it converge to a static solution, <a target="_blank" href="https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_harmonic_oscillator">
                        damping</a> is added to the distance constraints.  The <b>Damping</b> slider allows you to control the amount of damping
                    present in the simulation, from 0 (no damping) to 1 (critical damping).  Decreasing damping makes the simulation more "springy".
                    It may be useful to temporarily turn down damping to help the simulation more quickly converge towards its static solution - especially
                    for patterns that take a long time to curl.
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                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
<div class="modal fade" id="aboutDynamicSimModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
                <p><b>Compliant Dynamic Simulation</b><br/><br/>
                    ....
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
<div class="modal fade" id="aboutStaticSimModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
                <p><b>Compliant Static Simulation</b><br/><br/>
                    ....
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="aboutRigidSimModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
                <p><b>Rigid Static Simulation</b><br/><br/>
                    ....
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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<div class="modal fade" id="aboutAxialStrainModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-med">
        <div class="modal-content">
            <div class="modal-body">
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                  <span aria-hidden="true">&times;</span>
                </button>
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                <p><b>Strain Visualization</b><br/><br/>
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                    ....
                </p>
            </div>
        </div><!-- /.modal-content -->
    </div><!-- /.modal-dialog -->
</div><!-- /.modal -->
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</body>
</html>