298 lines
9.2 KiB
JavaScript
298 lines
9.2 KiB
JavaScript
'use strict';
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// Math helper - used mainly in hit test implementation done by webxr-test.js
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class XRMathHelper {
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static toString(p) {
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return "[" + p.x + "," + p.y + "," + p.z + "," + p.w + "]";
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}
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static transform_by_matrix(matrix, point) {
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return {
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x : matrix[0] * point.x + matrix[4] * point.y + matrix[8] * point.z + matrix[12] * point.w,
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y : matrix[1] * point.x + matrix[5] * point.y + matrix[9] * point.z + matrix[13] * point.w,
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z : matrix[2] * point.x + matrix[6] * point.y + matrix[10] * point.z + matrix[14] * point.w,
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w : matrix[3] * point.x + matrix[7] * point.y + matrix[11] * point.z + matrix[15] * point.w,
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};
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}
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static neg(p) {
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return {x : -p.x, y : -p.y, z : -p.z, w : p.w};
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}
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static sub(lhs, rhs) {
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// .w is treated here like an entity type, 1 signifies points, 0 signifies vectors.
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// point - point, point - vector, vector - vector are ok, vector - point is not.
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if (lhs.w != rhs.w && lhs.w == 0.0) {
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throw new Error("vector - point not allowed: " + toString(lhs) + "-" + toString(rhs));
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}
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return {x : lhs.x - rhs.x, y : lhs.y - rhs.y, z : lhs.z - rhs.z, w : lhs.w - rhs.w};
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}
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static add(lhs, rhs) {
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if (lhs.w == rhs.w && lhs.w == 1.0) {
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throw new Error("point + point not allowed", p1, p2);
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}
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return {x : lhs.x + rhs.x, y : lhs.y + rhs.y, z : lhs.z + rhs.z, w : lhs.w + rhs.w};
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}
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static cross(lhs, rhs) {
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if (lhs.w != 0.0 || rhs.w != 0.0) {
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throw new Error("cross product not allowed: " + toString(lhs) + "x" + toString(rhs));
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}
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return {
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x : lhs.y * rhs.z - lhs.z * rhs.y,
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y : lhs.z * rhs.x - lhs.x * rhs.z,
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z : lhs.x * rhs.y - lhs.y * rhs.x,
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w : 0
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};
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}
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static dot(lhs, rhs) {
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if (lhs.w != 0 || rhs.w != 0) {
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throw new Error("dot product not allowed: " + toString(lhs) + "x" + toString(rhs));
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}
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return lhs.x * rhs.x + lhs.y * rhs.y + lhs.z * rhs.z;
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}
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static mul(scalar, vector) {
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if (vector.w != 0) {
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throw new Error("scalar * vector not allowed", scalar, vector);
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}
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return {x : vector.x * scalar, y : vector.y * scalar, z : vector.z * scalar, w : vector.w};
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}
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static length(vector) {
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return Math.sqrt(XRMathHelper.dot(vector, vector));
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}
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static normalize(vector) {
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const l = XRMathHelper.length(vector);
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return XRMathHelper.mul(1.0/l, vector);
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}
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// All |face|'s points and |point| must be co-planar.
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static pointInFace(point, face) {
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const normalize = XRMathHelper.normalize;
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const sub = XRMathHelper.sub;
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const length = XRMathHelper.length;
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const cross = XRMathHelper.cross;
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let onTheRight = null;
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let previous_point = face[face.length - 1];
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// |point| is in |face| if it's on the same side of all the edges.
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for (let i = 0; i < face.length; ++i) {
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const current_point = face[i];
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const edge_direction = normalize(sub(current_point, previous_point));
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const turn_direction = normalize(sub(point, current_point));
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const sin_turn_angle = length(cross(edge_direction, turn_direction));
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if (onTheRight == null) {
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onTheRight = sin_turn_angle >= 0;
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} else {
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if (onTheRight && sin_turn_angle < 0) return false;
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if (!onTheRight && sin_turn_angle > 0) return false;
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}
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previous_point = current_point;
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}
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return true;
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}
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static det2x2(m00, m01, m10, m11) {
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return m00 * m11 - m01 * m10;
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}
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static det3x3(
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m00, m01, m02,
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m10, m11, m12,
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m20, m21, m22
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){
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const det2x2 = XRMathHelper.det2x2;
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return m00 * det2x2(m11, m12, m21, m22)
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- m01 * det2x2(m10, m12, m20, m22)
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+ m02 * det2x2(m10, m11, m20, m21);
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}
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static det4x4(
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m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33
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) {
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const det3x3 = XRMathHelper.det3x3;
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return m00 * det3x3(m11, m12, m13,
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m21, m22, m23,
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m31, m32, m33)
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- m01 * det3x3(m10, m12, m13,
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m20, m22, m23,
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m30, m32, m33)
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+ m02 * det3x3(m10, m11, m13,
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m20, m21, m23,
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m30, m31, m33)
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- m03 * det3x3(m10, m11, m12,
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m20, m21, m22,
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m30, m31, m32);
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}
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static inv2(m) {
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// mij - i-th column, j-th row
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const m00 = m[0], m01 = m[1], m02 = m[2], m03 = m[3];
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const m10 = m[4], m11 = m[5], m12 = m[6], m13 = m[7];
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const m20 = m[8], m21 = m[9], m22 = m[10], m23 = m[11];
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const m30 = m[12], m31 = m[13], m32 = m[14], m33 = m[15];
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const det = det4x4(
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m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33
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);
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}
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static transpose(m) {
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const result = Array(16);
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for (let i = 0; i < 4; i++) {
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for (let j = 0; j < 4; j++) {
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result[i * 4 + j] = m[j * 4 + i];
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}
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}
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return result;
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}
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// Inverts the matrix, ported from transformation_matrix.cc.
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static inverse(m) {
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const det3x3 = XRMathHelper.det3x3;
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// mij - i-th column, j-th row
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const m00 = m[0], m01 = m[1], m02 = m[2], m03 = m[3];
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const m10 = m[4], m11 = m[5], m12 = m[6], m13 = m[7];
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const m20 = m[8], m21 = m[9], m22 = m[10], m23 = m[11];
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const m30 = m[12], m31 = m[13], m32 = m[14], m33 = m[15];
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const det = XRMathHelper.det4x4(
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m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33
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);
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if (Math.abs(det) < 0.0001) {
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return null;
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}
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const invDet = 1.0 / det;
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// Calculate `comatrix * 1/det`:
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const result2 = [
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// First column (m0r):
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invDet * det3x3(m11, m12, m13, m21, m22, m23, m32, m32, m33),
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-invDet * det3x3(m10, m12, m13, m20, m22, m23, m30, m32, m33),
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invDet * det3x3(m10, m11, m13, m20, m21, m23, m30, m31, m33),
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-invDet * det3x3(m10, m11, m12, m20, m21, m22, m30, m31, m32),
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// Second column (m1r):
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-invDet * det3x3(m01, m02, m03, m21, m22, m23, m32, m32, m33),
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invDet * det3x3(m00, m02, m03, m20, m22, m23, m30, m32, m33),
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-invDet * det3x3(m00, m01, m03, m20, m21, m23, m30, m31, m33),
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invDet * det3x3(m00, m01, m02, m20, m21, m22, m30, m31, m32),
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// Third column (m2r):
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invDet * det3x3(m01, m02, m03, m11, m12, m13, m31, m32, m33),
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-invDet * det3x3(m00, m02, m03, m10, m12, m13, m30, m32, m33),
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invDet * det3x3(m00, m01, m03, m10, m11, m13, m30, m31, m33),
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-invDet * det3x3(m00, m01, m02, m10, m11, m12, m30, m31, m32),
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// Fourth column (m3r):
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-invDet * det3x3(m01, m02, m03, m11, m12, m13, m21, m22, m23),
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invDet * det3x3(m00, m02, m03, m10, m12, m13, m20, m22, m23),
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-invDet * det3x3(m00, m01, m03, m10, m11, m13, m20, m21, m23),
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invDet * det3x3(m00, m01, m02, m10, m11, m12, m20, m21, m22),
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];
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// Actual inverse is `1/det * transposed(comatrix)`:
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return XRMathHelper.transpose(result2);
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}
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static mul4x4(m1, m2) {
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if (m1 == null || m2 == null) {
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return null;
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}
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const result = Array(16);
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for (let row = 0; row < 4; row++) {
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for (let col = 0; col < 4; col++) {
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result[4 * col + row] = 0;
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for(let i = 0; i < 4; i++) {
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result[4 * col + row] += m1[4 * i + row] * m2[4 * col + i];
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}
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}
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}
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return result;
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}
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// Decomposes a matrix, with the assumption that the passed in matrix is
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// a rigid transformation (i.e. position and rotation *only*!).
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// The result is an object with `position` and `orientation` keys, which should
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// be compatible with FakeXRRigidTransformInit.
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// The implementation should match the behavior of gfx::Transform, but assumes
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// that scale, skew & perspective are not present in the matrix so it could be
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// simplified.
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static decomposeRigidTransform(m) {
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const m00 = m[0], m01 = m[1], m02 = m[2], m03 = m[3];
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const m10 = m[4], m11 = m[5], m12 = m[6], m13 = m[7];
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const m20 = m[8], m21 = m[9], m22 = m[10], m23 = m[11];
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const m30 = m[12], m31 = m[13], m32 = m[14], m33 = m[15];
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const position = [m30, m31, m32];
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const orientation = [0, 0, 0, 0];
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const trace = m00 + m11 + m22;
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if (trace > 0) {
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const S = Math.sqrt(trace + 1) * 2;
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orientation[3] = 0.25 * S;
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orientation[0] = (m12 - m21) / S;
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orientation[1] = (m20 - m02) / S;
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orientation[2] = (m01 - m10) / S;
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} else if (m00 > m11 && m00 > m22) {
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const S = Math.sqrt(1.0 + m00 - m11 - m22) * 2;
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orientation[3] = (m12 - m21) / S;
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orientation[0] = 0.25 * S;
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orientation[1] = (m01 + m10) / S;
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orientation[2] = (m20 + m02) / S;
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} else if (m11 > m22) {
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const S = Math.sqrt(1.0 + m11 - m00 - m22) * 2;
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orientation[3] = (m20 - m02) / S;
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orientation[0] = (m01 + m10) / S;
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orientation[1] = 0.25 * S;
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orientation[2] = (m12 + m21) / S;
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} else {
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const S = Math.sqrt(1.0 + m22 - m00 - m11) * 2;
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orientation[3] = (m01 - m10) / S;
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orientation[0] = (m20 + m02) / S;
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orientation[1] = (m12 + m21) / S;
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orientation[2] = 0.25 * S;
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}
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return { position, orientation };
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}
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static identity() {
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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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0, 0, 0, 1
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];
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};
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}
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XRMathHelper.EPSILON = 0.001;
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