Source code
Revision control
Copy as Markdown
Other Tools
'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;