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