285 lines
No EOL
9.4 KiB
JavaScript
285 lines
No EOL
9.4 KiB
JavaScript
var MDN = MDN || {};
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MDN.matrixArrayToCssMatrix = function (array) {
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return "matrix3d(" + array.join(',') + ")";
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}
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MDN.multiplyPoint = function (matrix, point) {
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var x = point[0], y = point[1], z = point[2], w = point[3];
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var c1r1 = matrix[ 0], c2r1 = matrix[ 1], c3r1 = matrix[ 2], c4r1 = matrix[ 3],
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c1r2 = matrix[ 4], c2r2 = matrix[ 5], c3r2 = matrix[ 6], c4r2 = matrix[ 7],
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c1r3 = matrix[ 8], c2r3 = matrix[ 9], c3r3 = matrix[10], c4r3 = matrix[11],
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c1r4 = matrix[12], c2r4 = matrix[13], c3r4 = matrix[14], c4r4 = matrix[15];
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return [
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x*c1r1 + y*c1r2 + z*c1r3 + w*c1r4,
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x*c2r1 + y*c2r2 + z*c2r3 + w*c2r4,
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x*c3r1 + y*c3r2 + z*c3r3 + w*c3r4,
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x*c4r1 + y*c4r2 + z*c4r3 + w*c4r4
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];
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}
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MDN.multiplyMatrices = function (a, b) {
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// TODO - Simplify for explanation
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// currently taken from https://github.com/toji/gl-matrix/blob/master/src/gl-matrix/mat4.js#L306-L337
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var result = [];
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var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
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// Cache only the current line of the second matrix
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var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
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result[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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result[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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result[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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result[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
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result[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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result[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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result[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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result[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
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result[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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result[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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result[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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result[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
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result[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
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result[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
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result[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
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result[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
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return result;
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}
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MDN.multiplyArrayOfMatrices = function (matrices) {
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var inputMatrix = matrices[0];
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for(var i=1; i < matrices.length; i++) {
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inputMatrix = MDN.multiplyMatrices(inputMatrix, matrices[i]);
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}
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return inputMatrix;
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}
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MDN.normalMatrix = function (matrix) {
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/*
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This function takes the inverse and then transpose of the provided
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4x4 matrix. The result is a 3x3 matrix. Essentially the translation
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part of the matrix gets removed.
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https://github.com/toji/gl-matrix
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*/
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var a00 = matrix[0], a01 = matrix[1], a02 = matrix[2], a03 = matrix[3],
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a10 = matrix[4], a11 = matrix[5], a12 = matrix[6], a13 = matrix[7],
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a20 = matrix[8], a21 = matrix[9], a22 = matrix[10], a23 = matrix[11],
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a30 = matrix[12], a31 = matrix[13], a32 = matrix[14], a33 = matrix[15],
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b00 = a00 * a11 - a01 * a10,
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b01 = a00 * a12 - a02 * a10,
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b02 = a00 * a13 - a03 * a10,
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b03 = a01 * a12 - a02 * a11,
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b04 = a01 * a13 - a03 * a11,
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b05 = a02 * a13 - a03 * a12,
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b06 = a20 * a31 - a21 * a30,
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b07 = a20 * a32 - a22 * a30,
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b08 = a20 * a33 - a23 * a30,
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b09 = a21 * a32 - a22 * a31,
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b10 = a21 * a33 - a23 * a31,
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b11 = a22 * a33 - a23 * a32,
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// Calculate the determinant
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det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
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if (!det) {
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return null;
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}
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det = 1.0 / det;
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var result = []
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result[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
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result[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
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result[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
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result[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
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result[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
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result[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
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result[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
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result[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
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result[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
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return result;
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}
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MDN.rotateXMatrix = function (a) {
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var cos = Math.cos;
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var sin = Math.sin;
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return [
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1, 0, 0, 0,
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0, cos(a), -sin(a), 0,
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0, sin(a), cos(a), 0,
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0, 0, 0, 1
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];
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}
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MDN.rotateYMatrix = function (a) {
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var cos = Math.cos;
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var sin = Math.sin;
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return [
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cos(a), 0, sin(a), 0,
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0, 1, 0, 0,
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-sin(a), 0, cos(a), 0,
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0, 0, 0, 1
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];
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}
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MDN.rotateZMatrix = function (a) {
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var cos = Math.cos;
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var sin = Math.sin;
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return [
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cos(a), -sin(a), 0, 0,
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sin(a), cos(a), 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1
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];
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}
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MDN.translateMatrix = function (x, y, z) {
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return [
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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x, y, z, 1
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];
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}
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MDN.scaleMatrix = function (w, h, d) {
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return [
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w, 0, 0, 0,
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0, h, 0, 0,
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0, 0, d, 0,
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0, 0, 0, 1
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];
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}
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MDN.perspectiveMatrix = function (fieldOfViewInRadians, aspectRatio, near, far) {
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// Construct a perspective matrix
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/*
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Field of view - the angle in radians of what's in view along the Y axis
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Aspect Ratio - the ratio of the canvas, typically canvas.width / canvas.height
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Near - Anything before this point in the Z direction gets clipped (resultside of the clip space)
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Far - Anything after this point in the Z direction gets clipped (outside of the clip space)
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*/
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var f = 1.0 / Math.tan(fieldOfViewInRadians / 2);
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var rangeInv = 1 / (near - far);
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return [
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f / aspectRatio, 0, 0, 0,
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0, f, 0, 0,
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0, 0, (near + far) * rangeInv, -1,
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0, 0, near * far * rangeInv * 2, 0
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];
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}
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MDN.orthographicMatrix = function(left, right, bottom, top, near, far) {
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// Each of the parameters represents the plane of the bounding box
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var lr = 1 / (left - right);
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var bt = 1 / (bottom - top);
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var nf = 1 / (near - far);
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var row4col1 = (left + right) * lr;
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var row4col2 = (top + bottom) * bt;
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var row4col3 = (far + near) * nf;
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return [
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-2 * lr, 0, 0, 0,
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0, -2 * bt, 0, 0,
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0, 0, 2 * nf, 0,
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row4col1, row4col2, row4col3, 1
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];
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}
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MDN.normalize = function( vector ) {
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// A utility function to make a vector have a length of 1
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var length = Math.sqrt(
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vector[0] * vector[0] +
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vector[1] * vector[1] +
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vector[2] * vector[2]
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)
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return [
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vector[0] / length,
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vector[1] / length,
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vector[2] / length
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]
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}
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MDN.invertMatrix = function( matrix ) {
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// Adapted from: https://github.com/mrdoob/three.js/blob/master/src/math/Matrix4.js
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// Performance note: Try not to allocate memory during a loop. This is done here
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// for the ease of understanding the code samples.
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var result = [];
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var n11 = matrix[0], n12 = matrix[4], n13 = matrix[ 8], n14 = matrix[12];
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var n21 = matrix[1], n22 = matrix[5], n23 = matrix[ 9], n24 = matrix[13];
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var n31 = matrix[2], n32 = matrix[6], n33 = matrix[10], n34 = matrix[14];
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var n41 = matrix[3], n42 = matrix[7], n43 = matrix[11], n44 = matrix[15];
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result[ 0] = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44;
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result[ 4] = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44;
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result[ 8] = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44;
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result[12] = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
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result[ 1] = n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44;
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result[ 5] = n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44;
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result[ 9] = n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44;
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result[13] = n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34;
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result[ 2] = n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44;
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result[ 6] = n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44;
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result[10] = n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44;
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result[14] = n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34;
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result[ 3] = n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43;
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result[ 7] = n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43;
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result[11] = n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43;
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result[15] = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33;
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var determinant = n11 * result[0] + n21 * result[4] + n31 * result[8] + n41 * result[12];
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if ( determinant === 0 ) {
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throw new Error("Can't invert matrix, determinant is 0");
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}
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for( var i=0; i < result.length; i++ ) {
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result[i] /= determinant;
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}
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return result;
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} |