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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>
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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">
        void main(){
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            gl_FragColor = vec4(0.0);
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        }
    </script>

    <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, creaseMeta2Index, numCreases]
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        uniform sampler2D u_beamMeta;//[k, d, length, otherNodeIndex]
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        uniform sampler2D u_creaseMeta;//[k, d, targetTheta]
        uniform sampler2D u_creaseMeta2;//[creaseIndex, momentArmLength, nodeIndex]
        uniform sampler2D u_normals;
        uniform sampler2D u_theta;//[theta, z, normal1Index, normal2Index]
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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 creaseMeta2 = texture2D(u_creaseMeta2, scaledNodeCreaseIndex);//[creaseIndex, length to node, nodeType (1 or 2), isReaction]
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                float creaseIndex1D = creaseMeta2[0];
                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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                float targetTheta = creaseMeta[2] * u_creasePercent;
                float angForce = creaseMeta[0]*(targetTheta-thetas[0]);// + creaseMeta[1]*thetas[1];

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                if (creaseMeta2[3] < 0.0){//crease reaction
                    float nodeNum = creaseMeta2[2];

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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 momentArm1 = creaseMeta2[1];
                    float momentArm2 = creaseMeta2[2];
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                    vec3 _force = -0.5*(angForce/momentArm1*normal1 + angForce/momentArm2*normal2);
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                    force += _force;
                } else {
                    float nodeNum = creaseMeta2[2];
                    float normalIndex1D = thetas[2];//node #1
                    if (nodeNum > 1.1) {
                        normalIndex1D = thetas[3];//node #2
                    }
                    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;

                    float momentArm = creaseMeta2[1];

                    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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            //float theta = acos(dotNormals);
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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);

            //float sign = dot(cross(normal1, normal2), creaseVector);
            //if (sign < 0.0) theta *= -1.0;
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            float diff = theta-lastTheta[0];
            float projectedTheta = lastTheta[0] + lastTheta[1]*u_dt;
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            if (diff < -5.0) {
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                diff += TWO_PI;
                theta = lastTheta[0] + diff;
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            } else if (diff > 5.0) {
                diff  -= TWO_PI;
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                theta = lastTheta[0] + diff;
            }
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            gl_FragColor = vec4(theta, creaseVectorIndices[1], 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;

            gl_FragColor = vec4(normalize(cross(b-a, c-a)), 0.0);
        }
    </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/OrthographicTrackballControls.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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                    <li class="dropdown-submenu">
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                    <!--<li><a id="saveSVG" href="#">Save Pattern as SVG...</a></li>-->
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            <li><a id="navPattern" href="#">Pattern</a></li>
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        <!--<form class="navbar-form navbar-right" action="#" role="search">-->
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<div id="controls">
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    <b>Simulation Type:</b><br/>
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    <div class="indent">
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            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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            Compliant Static Simulation (not finished yet) <a class="about floatRight" href="#" id="aboutStaticSim"><span class="fui-question-circle"></span></a>
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        </label>
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    <b>Stiffness Settings:</b><a class="floatRight about" href="#" id="aboutStiffness"><span class="fui-question-circle"></span></a><br/><br/>
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    <div class="sliderInput" id="axialStiffness">
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        <input value="" placeholder="" class="form-control" type="text">
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        <span class="label-slider">Fold Stiffness : </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">
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        <span class="label-slider">Facet Stiffness : </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">
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    <div class="sliderInput" id="percentDamping">
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        <input value="" placeholder="" class="form-control" type="text">
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    <br/><br/>
    <b>Error:</b><br/>
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    <div class="indent">
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        <label>Average node error: <span id="globalError"></span></label>
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        <a class="about floatRight" href="#" id="aboutError"><span class="fui-question-circle"></span></a>
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    </div><br/>
    <b>Animation Settings:</b><br/>
    <span class="floatRight">&Delta; t = <span id="deltaT"></span> seconds</span><br/><br/>
    <a href="#" id="reset" class="btn btn-lg btn-default">Reset</a>
    <a href="#" id="start" class="btn btn-lg btn-success">Start Simulation</a>
    <a href="#" id="pause" class="btn btn-lg btn-warning">Pause Simulation</a>
    <br/><br/>
    <div id="stepForwardOptions" class="floatRight">
        Num Steps: &nbsp;&nbsp;<input id="numSteps" value="100" placeholder="" class="form-control" type="text">
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    </div>
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    <br/><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">
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        <b>View Settings:</b><br/><br/>
        <div class="indent">
            Mesh Material:
            <div class="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">
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                        <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
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                        <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
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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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                        Axial 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>
            </div><br/>
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            Edges:
            <div class="indent">
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                    Edges Visible
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                <div id="edgeVisOptions" class="indent">
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                        <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>
                        Mountains
                    </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>
                        Valleys
                    </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
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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>
                        Undriven Edges
                    </label>
                </div>
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            </div><br/>
            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
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            </div>
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                <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/>
                    <a target="_blank" href="https://github.com/mapbox/earcut">Earcut Library</a><br/>
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                <br/><br/>
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                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>.
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                Code available on <a href="https://github.com/amandaghassaei/OrigamiSimulator" target="_blank">Github</a>.
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                <p><b>Export STL</b><br/><br/>
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                    settings:<br/>
                    single sided/double sided<br/>
                    scale
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                </p>
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<div class="modal fade" id="importFoldModal" tabindex="-1" role="dialog">
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                <p><b>Import FOLD</b><br/><br/>
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                <label class="checkbox" for="foldUseAngles">
                    <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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                </p>
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                <button data-dismiss="modal" type="button" class="btn btn-success">OK</button>
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                <p><b>Simulation Error</b><br/><br/>
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                    "Average node error" gives a sense of how much the distance constraints in the
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                    origami pattern are being violated.  The error at each node is evaluated by averaging the
                    percent deviation of all its distance constraints with adjacent nodes.  This error is
                    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">
                        Cauchy strain or engineering strain</a> of the axial constraints on this system.
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                    Increasing the "Axial Stiffness" 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 node graphically, select "Axial Strain Visualization" under "Mesh Material"
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                     in the left menu.
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