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    <title>Origami Simulator</title>

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

    <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;

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

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

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

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

        vec4 getFromArray(float index1D, vec2 dimensions, sampler2D tex){
            vec2 index = vec2(mod(index1D, dimensions.x)+0.5, floor(index1D/dimensions.x)+0.5);
            vec2 scaledIndex = index/dimensions;
            return texture2D(tex, scaledIndex);
        }

        vec3 getPosition(float index1D){
            vec2 index = vec2(mod(index1D, u_textureDim.x)+0.5, floor(index1D/u_textureDim.x)+0.5);
            vec2 scaledIndex = index/u_textureDim;
            return texture2D(u_lastPosition, scaledIndex).xyz + texture2D(u_originalPosition, scaledIndex).xyz;
        }

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

            vec2 mass = texture2D(u_mass, scaledFragCoord).xy;
            if (mass[1] == 1.0){//fixed
                gl_FragColor = vec4(0.0);
                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);
            vec4 meta = texture2D(u_meta, scaledFragCoord);
            vec2 meta2 = texture2D(u_meta2, scaledFragCoord).xy;

            float nodeError = 0.0;

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

                vec4 beamMeta = getFromArray(meta[0]+float(j), u_textureDimEdges, u_beamMeta);

                float neighborIndex1D = beamMeta[3];
                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;
                float deltaPLength = length(deltaP);
                deltaP -= deltaP*(beamMeta[2]/deltaPLength);
                nodeError += abs(deltaPLength/length(nominalDist) - 1.0);
                vec3 deltaV = neighborLastVelocity-lastVelocity;

                vec3 _force = deltaP*beamMeta[0] + deltaV*beamMeta[1];
                force += _force;
            }
            nodeError /= meta[1];

            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;

                vec4 nodeCreaseMeta = getFromArray(meta[2]+float(j), u_textureDimNodeCreases, u_nodeCreaseMeta);

                float creaseIndex1D = nodeCreaseMeta[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]
                vec4 creaseGeo = texture2D(u_creaseGeo, scaledCreaseIndex);//[h1, h2, coef1, coef2]
                if (creaseGeo[0]< 0.0) continue;//crease disabled bc it has collapsed too much

                float targetTheta = creaseMeta[2] * u_creasePercent;
                float angForce = creaseMeta[0]*(targetTheta-thetas[0]);// + creaseMeta[1]*thetas[1];

                float nodeNum = nodeCreaseMeta[1];//1, 2, 3, 4

                if (nodeNum > 2.0){//crease reaction, node is on a crease

                    //node #1
                    vec3 normal1 = getFromArray(thetas[2], u_textureDimFaces, u_normals).xyz;

                    //node #2
                    vec3 normal2 = getFromArray(thetas[3], u_textureDimFaces, u_normals).xyz;

                    float coef1 = creaseGeo[2];
                    float coef2 = creaseGeo[3];

                    if (nodeNum == 3.0){
                        coef1 = 1.0-coef1;
                        coef2 = 1.0-coef2;
                    }

                    vec3 _force = -angForce*(coef1/creaseGeo[0]*normal1 + coef2/creaseGeo[1]*normal2);
                    force += _force;

                } else {

                    float normalIndex1D = thetas[2];//node #1
                    float momentArm = creaseGeo[0];//node #1
                    if (nodeNum == 2.0) {
                        normalIndex1D = thetas[3];//node #2
                        momentArm = creaseGeo[1];//node #2
                    }

                    vec3 normal = getFromArray(normalIndex1D, u_textureDimFaces, u_normals).xyz;

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

            for (int j=0;j<100;j++){//for all faces (up to 100, had to put a const int in here)
                if (j >= int(meta2[1])) break;

                vec4 faceMeta = getFromArray(meta2[0]+float(j), u_textureDimNodeFaces, u_nodeFaceMeta);//[face index, a, b, c]
                vec3 nominalAngles = getFromArray(faceMeta[0], u_textureDimFaces, u_nominalTriangles).xyz;//[angA, angB, angC]

                int faceIndex = 0;
                if (faceMeta[2] < 0.0) faceIndex = 1;
                if (faceMeta[3] < 0.0) faceIndex = 2;

                //get node positions
                vec3 a = faceIndex == 0 ? lastPosition+originalPosition : getPosition(faceMeta[1]);
                vec3 b = faceIndex == 1 ? lastPosition+originalPosition : getPosition(faceMeta[2]);
                vec3 c = faceIndex == 2 ? lastPosition+originalPosition : getPosition(faceMeta[3]);

                //calc angles
                vec3 ab = b-a;
                vec3 ac = c-a;
                vec3 bc = c-b;

                float lengthAB = length(ab);
                float lengthAC = length(ac);
                float lengthBC = length(bc);

                float tol = 0.0000001;
                if (abs(lengthAB) < tol || abs(lengthBC) < tol || abs(lengthAC) < tol) continue;

                ab /= lengthAB;
                ac /= lengthAC;
                bc /= lengthBC;

                vec3 angles = vec3(acos(dot(ab, ac)),
                    acos(-1.0*dot(ab, bc)),
                    acos(dot(ac, bc)));
                vec3 anglesDiff = nominalAngles-angles;

                vec3 normal = getFromArray(faceMeta[0], u_textureDimFaces, u_normals).xyz;

                //calc forces
                anglesDiff *= u_axialStiffness/100.0;
                if (faceIndex == 0){//a
                    vec3 normalCrossAC = cross(normal, ac)/lengthAC;
                    vec3 normalCrossAB = cross(normal, ab)/lengthAB;
                    force -= anglesDiff[0]*(normalCrossAC - normalCrossAB);
                    force -= anglesDiff[1]*normalCrossAB;
                    force += anglesDiff[2]*normalCrossAC;
                } else if (faceIndex == 1){
                    vec3 normalCrossAB = cross(normal, ab)/lengthAB;
                    vec3 normalCrossBC = cross(normal, bc)/lengthBC;
                    force -= anglesDiff[0]*normalCrossAB;
                    force += anglesDiff[1]*(normalCrossAB + normalCrossBC);
                    force -= anglesDiff[2]*normalCrossBC;
                } else if (faceIndex == 2){
                    vec3 normalCrossAC = cross(normal, ac)/lengthAC;
                    vec3 normalCrossBC = cross(normal, bc)/lengthBC;
                    force += anglesDiff[0]*normalCrossAC;
                    force -= anglesDiff[1]*normalCrossBC;
                    force += anglesDiff[2]*(normalCrossBC - normalCrossAC);
                }

            }

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

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

        vec4 getFromArray(float index1D, vec2 dimensions, sampler2D tex){
            vec2 index = vec2(mod(index1D, dimensions.x)+0.5, floor(index1D/dimensions.x)+0.5);
            vec2 scaledIndex = index/dimensions;
            return texture2D(tex, scaledIndex);
        }

        void main(){

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

            vec4 lastTheta = texture2D(u_lastTheta, scaledFragCoord);

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

            vec3 normal1 = getFromArray(lastTheta[2], u_textureDimFaces, u_normals).xyz;
            vec3 normal2 = getFromArray(lastTheta[3], u_textureDimFaces, u_normals).xyz;

            float dotNormals = dot(normal1, normal2);//normals are already normalized, no need to divide by length
            if (dotNormals < -1.0) dotNormals = -1.0;
            else if (dotNormals > 1.0) dotNormals = 1.0;

            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;

            //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);

            float theta = atan(y, x);

            float diff = theta-lastTheta[0];
            float origDiff = diff;
            if (diff < -5.0) {
                diff += TWO_PI;
            } else if (diff > 5.0) {
                diff -= TWO_PI;
            }
            theta = lastTheta[0] + diff;
            gl_FragColor = vec4(theta, diff, lastTheta[2], lastTheta[3]);//[theta, w, normal1Index, normal2Index]
        }
    </script>

    <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;

        vec3 getPosition(float index1D){
            vec2 index = vec2(mod(index1D, u_textureDim.x)+0.5, floor(index1D/u_textureDim.x)+0.5);
            vec2 scaledIndex = index/u_textureDim;
            return texture2D(u_lastPosition, scaledIndex).xyz + texture2D(u_originalPosition, scaledIndex).xyz;
        }

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

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

            vec3 a = getPosition(indices[0]);
            vec3 b = getPosition(indices[1]);
            vec3 c = getPosition(indices[2]);

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

            gl_FragColor = vec4(normal, 0.0);
        }
    </script>

    <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;
        uniform sampler2D u_creaseMeta2;

        vec3 getPosition(float index1D){
            vec2 index = vec2(mod(index1D, u_textureDim.x)+0.5, floor(index1D/u_textureDim.x)+0.5);
            vec2 scaledIndex = index/u_textureDim;
            return texture2D(u_lastPosition, scaledIndex).xyz + texture2D(u_originalPosition, scaledIndex).xyz;
        }

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

            vec4 creaseMeta = texture2D(u_creaseMeta2, scaledFragCoord);

            vec3 node1 = getPosition(creaseMeta[0]);
            vec3 node2 = getPosition(creaseMeta[1]);
            vec3 node3 = getPosition(creaseMeta[2]);
            vec3 node4 = getPosition(creaseMeta[3]);

            float tol = 0.000001;

            vec3 creaseVector = node4-node3;
            float creaseLength = length(creaseVector);

            if (abs(creaseLength)<tol) {
                gl_FragColor = vec4(-1);//disable crease
                return;
            }
            creaseVector /= creaseLength;

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

            float proj1Length = dot(creaseVector, vector1);
            float proj2Length = dot(creaseVector, vector2);

            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));

            if (dist1<tol || dist2<tol){
                gl_FragColor = vec4(-1);//disable crease
                return;
            }

            gl_FragColor = vec4(dist1, dist2, proj1Length/creaseLength, proj2Length/creaseLength);
        }
    </script>

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        <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">
                    <li><a class="loadFile" href="#">Import... (SVG / FOLD)</a></li>
                    <!--<li><a id="importSettings" href="#">SVG Import Settings...</a></li>-->
                    <li><a id="tips" href="#">File Import Tips</a></li>
                    <li class="divider"></li>
                    <li><a id="createGif" href="#">Record animated GIF...</a></li>
                    <li><a id="createVideo" href="#">Record video...</a></li>
                    <li class="divider"></li>
                    <li><a id="exportFOLD" href="#">Save Simulation as FOLD...</a></li>
                    <li><a id="exportSTL" href="#">Save Simulation as STL...</a></li>
                    <li><a id="exportOBJ" href="#">Save Simulation as OBJ...</a></li>
                    <li class="divider"></li>
                    <li><a id="saveSVG" href="#">Save Pattern as SVG...</a></li>
                    <!--<li><a id="saveSVGScreenshot" href="#">Save SVG screenshot</a></li>-->
                </ul>
            </li>
            <li class="dropdown navDropdown">
                <a href="#" class="dropdown-toggle" data-toggle="dropdown">Examples <b class="caret"></b></a>
                <span class="dropdown-arrow"></span>
                <ul class="dropdown-menu" style="min-width: 200px;">
                    <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/flappingBird.svg">Flapping Bird</a></li>
                            <li><a href="#" class="demo author" data-author="randlett" data-url="Origami/randlettflappingbird.svg">Randlett Flapping Bird</a></li>
                            <li><a href="#" class="demo" data-url="Origami/traditionalCrane.svg">Crane</a></li>
                            <li><a href="#" class="demo author" data-author="hypar" data-url="Origami/hypar.svg">Hypar</a></li>
                            <li><a href="#" class="demo author" data-author="langTreemaker" data-url="Origami/langCardinal.svg">Lang Cardinal</a></li>
                            <li><a href="#" class="demo author" data-author="langTreemaker" data-url="Origami/langOrchid.svg">Lang Orchid</a></li>
                            <li><a href="#" class="demo author" data-author="langTreemaker" data-url="Origami/langKnlDragon.svg">Lang KNL Dragon</a></li>
                            <li><a href="#" class="demo" data-url="Origami/singlesquaretwist.svg">Square Twist (single)</a></li>
                            <li><a href="#" class="demo author" data-author="squareTwist" data-url="Origami/squaretwistManyAngles.svg">Square Twist (many angles)</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Tessellations<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo author" data-author="miuraOri" data-url="Tessellations/miura-ori.svg">Miura-Ori</a></li>
                            <li><a href="#" class="demo" data-url="Tessellations/waterbomb.svg">Waterbomb</a></li>
                            <li class="divider"></li>
                            <li><a href="#" class="demo author" data-author="huffmanTessellations" data-url="Tessellations/huffmanExtrudedBoxes.svg">Huffman Extruded Boxes</a></li>
                            <li><a href="#" class="demo author" data-author="huffmanTessellations" data-url="Tessellations/huffmanWaterbomb.svg">Huffman Waterbombs</a></li>
                            <li><a href="#" class="demo author" data-author="huffmanTessellations" data-url="Tessellations/huffmanRectangularWeave.svg">Huffman Rect Weave</a></li>
                            <li><a href="#" class="demo author" data-author="huffmanTessellations" data-url="Tessellations/huffmanStarsTriangles.svg">Huffman Stars-Triangles</a></li>
                            <li><a href="#" class="demo author" data-author="huffmanTessellations" data-url="Tessellations/huffmanExdentedBoxes.svg">Huffman Exdented Boxes</a></li>
                            <li class="divider"></li>
                            <li><a href="#" class="demo author" data-author="reschTessellations" data-url="Tessellations/reschTriTessellation.svg">Resch Triangle Tessellation</a></li>
                            <li><a href="#" class="demo author" data-author="reschTessellations" data-url="Tessellations/reschBarbell.svg">Resch Barbell Tessellation</a></li>
                            <li class="divider"></li>
                            <li><a href="#" class="demo author" data-author="langTessellations" data-url="Tessellations/langHoneycomb.svg">Lang Honeycomb Tessellation</a></li>
                            <li><a href="#" class="demo author" data-author="langTessellations" data-url="Tessellations/langWedgeDoubleFaced.svg">Lang Wedged Double Faced Tessellation</a></li>
                            <li><a href="#" class="demo author" data-author="langTessellations" data-url="Tessellations/langOvalTessellation.svg">Lang Oval Tessellation</a></li>
                            <li><a href="#" class="demo author" data-author="langTessellations" data-url="Tessellations/langHyperbolicLimit.svg">Lang Hyperbolic Limit</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Curved Creases<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo author" data-author="huffmanCurved" data-url="Curved/huffmanTower.svg">Huffman Tower</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Maze Foldings<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo author" data-author="squareMaze" data-url="Squaremaze/helloworld.svg">Square Maze "hello world"</a></li>
                            <li><a href="#" class="demo author" data-author="squareMaze" data-url="Squaremaze/origamisimulator.svg">Square Maze "origami simulator"</a></li>
                            <li><a href="#" class="demo author" data-author="squareMaze" data-url="Squaremaze/cross.svg">Square Maze "+"</a></li>
                            <!--<li class="divider"></li>-->
                        </ul>
                    </li>
                    <li class="divider"></li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Origami Bases<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo" data-url="Bases/birdBase.svg">Bird Base</a></li>
                            <li><a href="#" class="demo author" data-author="moveSlowly" data-url="Bases/frogBase.svg">Frog Base</a></li>
                            <li><a href="#" class="demo" data-url="Bases/boatBase.svg">Boat Base</a></li>
                            <li><a href="#" class="demo" data-url="Bases/pinwheelBase.svg">Pinwheel Base</a></li>
                            <li><a href="#" class="demo" data-url="Bases/openSinkBase.svg">Open Sink Base</a></li>
                            <li><a href="#" class="demo" data-url="Bases/squareBase.svg">Square Base</a></li>
                            <li><a href="#" class="demo" data-url="Bases/waterbombBase.svg">Waterbomb Base</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Simple Folds<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" class="demo" data-url="SimpleFolds/simpleVertex.svg">Simple Vertex</a></li>
                            <li><a href="#" class="demo" data-url="SimpleFolds/russianTriangle.svg">Russian Triangle</a></li>
                            <li><a href="#" class="demo" data-url="SimpleFolds/mapfold.svg">Map Fold</a></li>
                            <li><a href="#" class="demo" data-url="SimpleFolds/brochurefold.svg">Brochure Fold</a></li>
                        </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 author" data-author="skinnyTriangles" data-url="Tessellations/langRattanWeave.svg">Lang Rattan Weave</a></li>
                        </ul>
                    </li>
                </ul>
            </li>
            <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>
                    <li><a id="changeBackground" href="#">Change Background Color...</a></li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">Rotate Model<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a id="stopRotation" href="#">Stop Rotation</a></li>
                            <li><a id="rotateX" href="#">Rotate Around X</a></li>
                            <li><a id="rotateY" href="#">Rotate Around Y</a></li>
                            <li><a id="rotateZ" href="#">Rotate Around Z</a></li>
                            <li><a id="changeRotationSpeed" href="#">Change Rotation Speed...</a></li>
                        </ul>
                    </li>
                    <li class="dropdown-submenu">
                        <a tabindex="-1">View Direction<span class="pull-right fui-arrow-right"></span></a>
                        <ul class="dropdown-menu">
                            <li><a href="#" id="cameraZ">View Front</a></li>
                            <li><a href="#" id="cameraMinusZ">View Back</a></li>
                            <li><a href="#" id="cameraX">View Right</a></li>
                            <li><a href="#" id="cameraMinusX">View Left</a></li>
                            <li><a href="#" id="cameraY">View Top</a></li>
                            <li><a href="#" id="cameraMinusY">View Bottom</a></li>
                            <li><a href="#" id="cameraOrtho">View Ortho</a></li>
                        </ul>
                    </li>
                </ul>
            </li>
            <li><a id="navPattern" href="#">Pattern</a></li>
            <li><a id="navSimulation" href="#">Simulation</a></li>
            <li><a id="about" class="menuHoverControls" target="_blank" href="#">About</a></li>
        </ul>
        <!--<form class="navbar-form navbar-right" action="#" role="search">-->
            <!--<div class="form-group">-->
              <!--<div class="input-group">-->
                <div class="sliderInput floatRight" id="creasePercentNav">
                    <span class="label-slider">Fold Percent : </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>-->
            <!--</div>-->
        <!--</form>-->

    </div><!-- /.navbar-collapse -->
    <input id="fileSelector" type="file">

</nav>

<div  id="threeContainer"></div>
<canvas id="gpuMathCanvas"></canvas>
<div id="controls">
    <div class="sliderInput floatRight" id="creasePercent">
        <span class="label-slider">Fold Percent : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
        <input value="" placeholder="" class="float form-control" type="text">&nbsp;&nbsp;%
    </div><br/><br/>
    <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>
        <div id="stepForwardOptions" class="floatRight">
            <a href="#" id="stepForward" class="btn btn-lg btn-default">Step Forward</a>
            <label>Num Steps:</label> &nbsp;&nbsp;<input id="numSteps" value="100" placeholder="" class="int form-control" type="text">
            <br/><br/>
        </div>
    </div>
    <!--<b>Simulation Type:</b><br/>-->
    <!--<div class="indent">-->
        <!--<label class="radio">-->
            <!--<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>-->
        <!--</label>-->
        <!--&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/>-->
    <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">
                <span class="label-slider">Axial Stiffness : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>
                <input value="" placeholder="" class="float form-control" type="text">
            </div>
            <!--<div class="sliderInput paddingBottom" id="triStiffness">-->
                <!--<span class="label-slider">Triangle Stiffness : </span><div class="flat-slider ui-slider ui-corner-all ui-slider-horizontal ui-widget ui-widget-content"></div>-->
                <!--<input value="" placeholder="" class="float form-control" type="text">-->
            <!--</div>-->
            <div class="sliderInput" id="creaseStiffness">
                <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>
                <input value="" placeholder="" class="float form-control" type="text">
            </div>
            <div class="sliderInput" id="panelStiffness">
                <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>
                <input value="" placeholder="" class="float 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="float form-control" type="text">
            </div>
        </div><br/>
    </div>
    <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>
        </div>
    </div><br/>

    <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">
            <label>Average vertex error: <span id="globalError"></span></label>
        </div>
    </div><br/>

    <div class="extraSpace"></div>
</div>
<div id="svgViewer"></div>
<div id="controlsLeft" class="flipped">
    <div>
        <b>View Settings:</b><br/><br/>
        <div class="indent">
            <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">
                <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
                </label>
                <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="axialStrain" data-toggle="radio" class="custom-radio" type="radio"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                        Strain Visualization<a class="about floatRight" href="#" id="aboutAxialStrain"><span class="fui-question-circle"></span></a>
                    </label>
                    <div id="axialStrainMaterialOptions" class="indent">
                        <label>Max Strain: &nbsp;&nbsp;</label>
                        <input id="strainClip" value="" placeholder="" class="float 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>
                </div>
                <br/>
            </div><br/>
            <div>
                <a href="#" class="seeMore closed" data-id="edgeVisiblity"><span class="fui-triangle-down"></span>Edge Visiblity</a>:
            </div>
            <div id="edgeVisiblity" class="hide indent">
                <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>
                <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>
                        Mountains <span id="numMtns"></span>
                    </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 <span id="numValleys"></span>
                    </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>
                        Facet Creases <span id="numFacets"></span>
                    </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 <span id="numPassive"></span>
                    </label>
                    <label class="checkbox" for="boundaryEdgesVisible">
                        <input id="boundaryEdgesVisible" data-toggle="checkbox" class="custom-checkbox layersSelector" type="checkbox"><span class="icons"><span class="icon-unchecked"></span><span class="icon-checked"></span></span>
                        Boundary Edges <span id="numBoundary"></span>
                    </label>

                </div>
                <br/>
            </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-->
                <!--</label>-->
            <!--</div>-->
            <div>
                <a href="#" class="seeMore closed" data-id="virtualReality"><span class="fui-triangle-down"></span>Virtual Reality:</a>
            </div>
            <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>
                <div id="VRoptions"><br/>
                    <a href="#" id="enterVR" class="displayBlock btn btn-lg btn-inverse"></a>
                </div><br/><br/>
            </div><br/>
            <div class="extraSpace"></div>
        </div>
    </div>
</div>

<div class="modal fade" id="aboutModal" tabindex="-1" role="dialog">
    <div class="modal-dialog modal-lg">
        <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>ORIGAMI SIMULATOR</b><br/><br/>

                    This app allows you to upload any origami crease pattern and simulate how it will fold.  It iteratively solves for small displacements in the geometry of an initially flat sheet due to forces
                    exerted by creases.  This solver extends work from the following sources: <br/><br/>
                    &nbsp;&nbsp;&nbsp;&nbsp;<a target="_blank" href="http://www2.eng.cam.ac.uk/~sdg/preprint/5OSME.pdf">Origami Folding: A Structural Engineering Approach</a> by Mark Schenk and Simon D. Guest<br/>
                    &nbsp;&nbsp;&nbsp;&nbsp;<a target="_blank" href="http://www.tsg.ne.jp/TT/cg/TachiFreeformOrigami2010.pdf">Freeform Variations of Origami</a> by Tomohiro Tachi<br/>
                    <br/>
                    All simulation methods were written from scratch and are executed in parallel in several GPU fragment shaders for fast performance.
                </p><br/>
                    <b>Instructions:</b><br/><br/>
                    <ul>
                        <li>Slide the <b>Fold Percent</b> slider to control the degree of folding of the pattern (100% is fully folded, 0% is unfolded,
                            and -100% is fully folded with the opposite mountain/valley assignments).</li>
                        <li>Drag to rotate the model, scroll to zoom.</li>
                        <li>Import other patterns under the <b>Examples</b> menu.</li>
                        <li>Upload your own crease patterns in SVG or FOLD formats, following <a href="#" class="goToImportInstructions">these instructions</a>.</li>
                        <li>Export FOLD files or 3D models ( STL or OBJ ) of the folded state of your design ( <b>File > Save Simulation as...</b> ).</li>
                        <li>Visualize the internal strain of the origami as it folds using the <b>Strain Visualization</b> in the left menu.</li>
                        <li>If you are working from a computer connected to a Vive, follow <a href="#" id="goToViveInstructions">these instructions</a>
                            to use this app in an interactive virtual reality mode.</li>
                    </ul>
                    <br/>

                    <b>External Libraries:</b><br/><br/>
                    <ul>
                        <li>All rendering and 3D interaction done with <a target="_blank" href="https://threejs.org/">three.js</a></li>
                        <li><a href="https://www.npmjs.com/package/path-data-polyfill" target="_blank">path-data-polyfill</a> helps with SVG parsing</li>
                        <li><a href="https://github.com/edemaine/fold" target="_blank">FOLD</a> is used as the internal data structure, and methods from the FOLD api are used for SVG parsing</li>
                        <li>Arbitrary polygonal faces of imported geometry are triangulated using the <a target="_blank" href="https://github.com/mapbox/earcut">Earcut Library</a></li>
                        <li><a target="_blank" href="https://jquery.com/">jQuery</a>, <a target="_blank" href="http://getbootstrap.com/">Bootstrap</a>, and the
                            <a target="_blank" href="http://designmodo.github.io/Flat-UI/">Flat UI theme</a> used to build the GUI</li>
                    </ul>
                <p>
                    <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
                    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!<br/>
                    <br/>
                    More documentation coming soon.
                </p>
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