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@@ -2,6 +2,7 @@
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* Copyright (c) 2017 mol* contributors, licensed under MIT, See LICENSE file for more info.
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*
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* @author David Sehnal <david.sehnal@gmail.com>
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+ * @author Alexander Rose <alexander.rose@weirdbyte.de>
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*/
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/*
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@@ -16,9 +17,11 @@
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* furnished to do so, subject to the following conditions:
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*/
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-export interface Mat4 { [d: number]: number, '@type': 'mat4' }
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-export interface Vec3 { [d: number]: number, '@type': 'vec3' | 'vec4' }
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-export interface Vec4 { [d: number]: number, '@type': 'vec4' }
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+export interface Mat4 extends Array<number> { [d: number]: number, '@type': 'mat4', length: 16 }
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+export interface Mat3 extends Array<number> { [d: number]: number, '@type': 'mat3', length: 9 }
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+export interface Vec3 extends Array<number> { [d: number]: number, '@type': 'vec3', length: 3 }
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+export interface Vec4 extends Array<number> { [d: number]: number, '@type': 'vec4', length: 4 }
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+export interface Quat extends Array<number> { [d: number]: number, '@type': 'quat', length: 4 }
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const enum EPSILON { Value = 0.000001 }
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@@ -26,6 +29,10 @@ export function Mat4() {
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return Mat4.zero();
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}
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+export function Quat() {
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+ return Quat.zero();
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+}
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+
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/**
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* Stores a 4x4 matrix in a column major (j * 4 + i indexing) format.
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*/
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@@ -77,7 +84,7 @@ export namespace Mat4 {
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mat[15] = 1;
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return mat;
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}
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-
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+
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export function ofRows(rows: number[][]): Mat4 {
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const out = zero();
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for (let i = 0; i < 4; i++) {
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@@ -105,6 +112,44 @@ export namespace Mat4 {
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a[4 * j + i] = value;
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}
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+ export function toArray(a: Mat4, out: Helpers.NumberArray, offset: number) {
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+ out[offset + 0] = a[0];
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+ out[offset + 1] = a[1];
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+ out[offset + 2] = a[2];
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+ out[offset + 3] = a[3];
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+ out[offset + 4] = a[4];
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+ out[offset + 5] = a[5];
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+ out[offset + 6] = a[6];
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+ out[offset + 7] = a[7];
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+ out[offset + 8] = a[8];
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+ out[offset + 9] = a[9];
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+ out[offset + 10] = a[10];
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+ out[offset + 11] = a[11];
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+ out[offset + 12] = a[12];
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+ out[offset + 13] = a[13];
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+ out[offset + 14] = a[14];
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+ out[offset + 15] = a[15];
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+ }
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+
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+ export function fromArray(a: Mat4, array: Helpers.NumberArray, offset: number) {
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+ a[0] = array[offset + 0]
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+ a[1] = array[offset + 1]
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+ a[2] = array[offset + 2]
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+ a[3] = array[offset + 3]
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+ a[4] = array[offset + 4]
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+ a[5] = array[offset + 5]
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+ a[6] = array[offset + 6]
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+ a[7] = array[offset + 7]
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+ a[8] = array[offset + 8]
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+ a[9] = array[offset + 9]
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+ a[10] = array[offset + 10]
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+ a[11] = array[offset + 11]
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+ a[12] = array[offset + 12]
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+ a[13] = array[offset + 13]
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+ a[14] = array[offset + 14]
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+ a[15] = array[offset + 15]
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+ }
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+
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export function copy(out: Mat4, a: Mat4) {
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out[0] = a[0];
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out[1] = a[1];
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@@ -129,6 +174,45 @@ export namespace Mat4 {
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return Mat4.copy(Mat4.zero(), a);
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}
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+ export function transpose(out: Mat4, a: Mat4) {
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+ // If we are transposing ourselves we can skip a few steps but have to cache some values
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+ if (out === a) {
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+ const a01 = a[1], a02 = a[2], a03 = a[3];
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+ const a12 = a[6], a13 = a[7];
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+ const a23 = a[11];
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+ out[1] = a[4];
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+ out[2] = a[8];
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+ out[3] = a[12];
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+ out[4] = a01;
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+ out[6] = a[9];
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+ out[7] = a[13];
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+ out[8] = a02;
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+ out[9] = a12;
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+ out[11] = a[14];
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+ out[12] = a03;
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+ out[13] = a13;
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+ out[14] = a23;
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+ } else {
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+ out[0] = a[0];
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+ out[1] = a[4];
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+ out[2] = a[8];
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+ out[3] = a[12];
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+ out[4] = a[1];
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+ out[5] = a[5];
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+ out[6] = a[9];
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+ out[7] = a[13];
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+ out[8] = a[2];
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+ out[9] = a[6];
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+ out[10] = a[10];
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+ out[11] = a[14];
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+ out[12] = a[3];
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+ out[13] = a[7];
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+ out[14] = a[11];
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+ out[15] = a[15];
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+ }
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+ return out;
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+ }
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+
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export function invert(out: Mat4, a: Mat4) {
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const 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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@@ -463,6 +547,213 @@ export namespace Mat4 {
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}
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return true;
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}
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+
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+ export function fromQuat(out: Mat4, q: Quat) {
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+ const x = q[0], y = q[1], z = q[2], w = q[3];
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+ const x2 = x + x;
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+ const y2 = y + y;
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+ const z2 = z + z;
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+
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+ const xx = x * x2;
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+ const yx = y * x2;
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+ const yy = y * y2;
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+ const zx = z * x2;
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+ const zy = z * y2;
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+ const zz = z * z2;
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+ const wx = w * x2;
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+ const wy = w * y2;
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+ const wz = w * z2;
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+
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+ out[0] = 1 - yy - zz;
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+ out[1] = yx + wz;
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+ out[2] = zx - wy;
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+ out[3] = 0;
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+
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+ out[4] = yx - wz;
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+ out[5] = 1 - xx - zz;
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+ out[6] = zy + wx;
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+ out[7] = 0;
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+
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+ out[8] = zx + wy;
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+ out[9] = zy - wx;
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+ out[10] = 1 - xx - yy;
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+ out[11] = 0;
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+
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+ out[12] = 0;
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+ out[13] = 0;
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+ out[14] = 0;
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+ out[15] = 1;
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+
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+ return out;
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+ }
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+
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+ /**
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+ * Generates a frustum matrix with the given bounds
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+ */
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+ export function frustum(out: Mat4, left: number, right: number, bottom: number, top: number, near: number, far: number) {
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+ let rl = 1 / (right - left);
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+ let tb = 1 / (top - bottom);
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+ let nf = 1 / (near - far);
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+ out[0] = (near * 2) * rl;
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+ out[1] = 0;
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+ out[2] = 0;
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+ out[3] = 0;
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+ out[4] = 0;
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+ out[5] = (near * 2) * tb;
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+ out[6] = 0;
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+ out[7] = 0;
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+ out[8] = (right + left) * rl;
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+ out[9] = (top + bottom) * tb;
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+ out[10] = (far + near) * nf;
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+ out[11] = -1;
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+ out[12] = 0;
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+ out[13] = 0;
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+ out[14] = (far * near * 2) * nf;
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+ out[15] = 0;
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+ return out;
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+ }
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+
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+ /**
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+ * Generates a perspective projection matrix with the given bounds
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+ */
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+ export function perspective(out: Mat4, fovy: number, aspect: number, near: number, far: number) {
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+ let f = 1.0 / Math.tan(fovy / 2);
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+ let nf = 1 / (near - far);
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+ out[0] = f / aspect;
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+ out[1] = 0;
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+ out[2] = 0;
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+ out[3] = 0;
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+ out[4] = 0;
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+ out[5] = f;
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+ out[6] = 0;
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+ out[7] = 0;
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+ out[8] = 0;
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+ out[9] = 0;
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+ out[10] = (far + near) * nf;
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+ out[11] = -1;
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+ out[12] = 0;
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+ out[13] = 0;
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+ out[14] = (2 * far * near) * nf;
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+ out[15] = 0;
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+ return out;
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+ }
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+
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+ /**
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+ * Generates a orthogonal projection matrix with the given bounds
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+ */
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+ export function ortho(out: Mat4, left: number, right: number, bottom: number, top: number, near: number, far: number) {
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+ let lr = 1 / (left - right);
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+ let bt = 1 / (bottom - top);
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+ let nf = 1 / (near - far);
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+ out[0] = -2 * lr;
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+ out[1] = 0;
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+ out[2] = 0;
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+ out[3] = 0;
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+ out[4] = 0;
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+ out[5] = -2 * bt;
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+ out[6] = 0;
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+ out[7] = 0;
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+ out[8] = 0;
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+ out[9] = 0;
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+ out[10] = 2 * nf;
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+ out[11] = 0;
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+ out[12] = (left + right) * lr;
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+ out[13] = (top + bottom) * bt;
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+ out[14] = (far + near) * nf;
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+ out[15] = 1;
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+ return out;
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+ }
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+
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+ /**
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+ * Generates a look-at matrix with the given eye position, focal point, and up axis
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+ */
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+ export function lookAt(out: Mat4, eye: Vec3, center: Vec3, up: Vec3) {
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+ let x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
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+ let eyex = eye[0];
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+ let eyey = eye[1];
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+ let eyez = eye[2];
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+ let upx = up[0];
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+ let upy = up[1];
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+ let upz = up[2];
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+ let centerx = center[0];
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+ let centery = center[1];
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+ let centerz = center[2];
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+
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+ if (Math.abs(eyex - centerx) < EPSILON.Value &&
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+ Math.abs(eyey - centery) < EPSILON.Value &&
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+ Math.abs(eyez - centerz) < EPSILON.Value
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+ ) {
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+ return setIdentity(out);
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+ }
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+
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+ z0 = eyex - centerx;
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+ z1 = eyey - centery;
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+ z2 = eyez - centerz;
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+
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+ len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
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+ z0 *= len;
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+ z1 *= len;
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+ z2 *= len;
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+
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+ x0 = upy * z2 - upz * z1;
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+ x1 = upz * z0 - upx * z2;
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+ x2 = upx * z1 - upy * z0;
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+ len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
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+ if (!len) {
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+ x0 = 0;
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+ x1 = 0;
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+ x2 = 0;
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+ } else {
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+ len = 1 / len;
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+ x0 *= len;
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+ x1 *= len;
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+ x2 *= len;
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+ }
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+
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+ y0 = z1 * x2 - z2 * x1;
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+ y1 = z2 * x0 - z0 * x2;
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+ y2 = z0 * x1 - z1 * x0;
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+
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+ len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
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+ if (!len) {
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+ y0 = 0;
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+ y1 = 0;
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+ y2 = 0;
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+ } else {
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+ len = 1 / len;
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+ y0 *= len;
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+ y1 *= len;
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+ y2 *= len;
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+ }
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+
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+ out[0] = x0;
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+ out[1] = y0;
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+ out[2] = z0;
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+ out[3] = 0;
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+ out[4] = x1;
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+ out[5] = y1;
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+ out[6] = z1;
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+ out[7] = 0;
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+ out[8] = x2;
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+ out[9] = y2;
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+ out[10] = z2;
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+ out[11] = 0;
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+ out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
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+ out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
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+ out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
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+ out[15] = 1;
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+
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+ return out;
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+ }
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+}
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+
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+export namespace Mat3 {
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+ export function zero(): Mat3 {
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+ // force double backing array by 0.1.
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+ const ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0];
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+ ret[0] = 0.0;
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+ return ret as any;
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+ }
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}
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export namespace Vec3 {
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@@ -488,6 +779,18 @@ export namespace Vec3 {
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return { x: v[0], y: v[1], z: v[2] };
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}
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+ export function fromArray(v: Vec3, array: Helpers.NumberArray, offset: number) {
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+ v[0] = array[offset + 0]
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+ v[1] = array[offset + 1]
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+ v[2] = array[offset + 2]
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+ }
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+
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+ export function toArray(v: Vec3, out: Helpers.NumberArray, offset: number) {
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+ out[offset + 0] = v[0]
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+ out[offset + 1] = v[1]
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+ out[offset + 2] = v[2]
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+ }
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+
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export function create(x: number, y: number, z: number): Vec3 {
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const out = zero();
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out[0] = x;
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@@ -668,6 +971,14 @@ export namespace Vec4 {
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return out;
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}
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+ export function copy(out: Vec4, a: Vec4) {
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+ out[0] = a[0];
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+ out[1] = a[1];
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+ out[2] = a[2];
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+ out[3] = a[3];
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+ return out;
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+ }
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+
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export function set(out: Vec4, x: number, y: number, z: number, w: number) {
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out[0] = x;
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out[1] = y;
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@@ -676,6 +987,14 @@ export namespace Vec4 {
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return out;
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}
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+ export function add(out: Quat, a: Quat, b: Quat) {
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+ out[0] = a[0] + b[0];
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+ out[1] = a[1] + b[1];
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+ out[2] = a[2] + b[2];
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+ out[3] = a[3] + b[3];
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+ return out;
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+ }
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+
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export function distance(a: Vec4, b: Vec4) {
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const x = b[0] - a[0],
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y = b[1] - a[1],
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@@ -716,4 +1035,354 @@ export namespace Vec4 {
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out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
|
|
|
return out;
|
|
|
}
|
|
|
+}
|
|
|
+
|
|
|
+export namespace Quat {
|
|
|
+ export function zero(): Quat {
|
|
|
+ // force double backing array by 0.1.
|
|
|
+ const ret = [0.1, 0, 0, 0];
|
|
|
+ ret[0] = 0.0;
|
|
|
+ return ret as any;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function identity(): Quat {
|
|
|
+ const out = zero();
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function create(x: number, y: number, z: number, w: number) {
|
|
|
+ const out = identity();
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = w;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function setAxisAngle(out: Quat, axis: Vec3, rad: number) {
|
|
|
+ rad = rad * 0.5;
|
|
|
+ let s = Math.sin(rad);
|
|
|
+ out[0] = s * axis[0];
|
|
|
+ out[1] = s * axis[1];
|
|
|
+ out[2] = s * axis[2];
|
|
|
+ out[3] = Math.cos(rad);
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Gets the rotation axis and angle for a given
|
|
|
+ * quaternion. If a quaternion is created with
|
|
|
+ * setAxisAngle, this method will return the same
|
|
|
+ * values as providied in the original parameter list
|
|
|
+ * OR functionally equivalent values.
|
|
|
+ * Example: The quaternion formed by axis [0, 0, 1] and
|
|
|
+ * angle -90 is the same as the quaternion formed by
|
|
|
+ * [0, 0, 1] and 270. This method favors the latter.
|
|
|
+ */
|
|
|
+ export function getAxisAngle(out_axis: Vec3, q: Quat) {
|
|
|
+ let rad = Math.acos(q[3]) * 2.0;
|
|
|
+ let s = Math.sin(rad / 2.0);
|
|
|
+ if (s !== 0.0) {
|
|
|
+ out_axis[0] = q[0] / s;
|
|
|
+ out_axis[1] = q[1] / s;
|
|
|
+ out_axis[2] = q[2] / s;
|
|
|
+ } else {
|
|
|
+ // If s is zero, return any axis (no rotation - axis does not matter)
|
|
|
+ out_axis[0] = 1;
|
|
|
+ out_axis[1] = 0;
|
|
|
+ out_axis[2] = 0;
|
|
|
+ }
|
|
|
+ return rad;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function multiply(out: Quat, a: Quat, b: Quat) {
|
|
|
+ let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
+ let bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
+
|
|
|
+ out[0] = ax * bw + aw * bx + ay * bz - az * by;
|
|
|
+ out[1] = ay * bw + aw * by + az * bx - ax * bz;
|
|
|
+ out[2] = az * bw + aw * bz + ax * by - ay * bx;
|
|
|
+ out[3] = aw * bw - ax * bx - ay * by - az * bz;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function rotateX(out: Quat, a: Quat, rad: number) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
+ let bx = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw + aw * bx;
|
|
|
+ out[1] = ay * bw + az * bx;
|
|
|
+ out[2] = az * bw - ay * bx;
|
|
|
+ out[3] = aw * bw - ax * bx;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function rotateY(out: Quat, a: Quat, rad: number) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
+ let by = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw - az * by;
|
|
|
+ out[1] = ay * bw + aw * by;
|
|
|
+ out[2] = az * bw + ax * by;
|
|
|
+ out[3] = aw * bw - ay * by;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function rotateZ(out: Quat, a: Quat, rad: number) {
|
|
|
+ rad *= 0.5;
|
|
|
+
|
|
|
+ let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
+ let bz = Math.sin(rad), bw = Math.cos(rad);
|
|
|
+
|
|
|
+ out[0] = ax * bw + ay * bz;
|
|
|
+ out[1] = ay * bw - ax * bz;
|
|
|
+ out[2] = az * bw + aw * bz;
|
|
|
+ out[3] = aw * bw - az * bz;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Calculates the W component of a quat from the X, Y, and Z components.
|
|
|
+ * Assumes that quaternion is 1 unit in length.
|
|
|
+ * Any existing W component will be ignored.
|
|
|
+ */
|
|
|
+ export function calculateW(out: Quat, a: Quat) {
|
|
|
+ let x = a[0], y = a[1], z = a[2];
|
|
|
+
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Performs a spherical linear interpolation between two quat
|
|
|
+ */
|
|
|
+ export function slerp(out: Quat, a: Quat, b: Quat, t: number) {
|
|
|
+ // benchmarks:
|
|
|
+ // http://jsperf.com/quaternion-slerp-implementations
|
|
|
+ let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
+ let bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
+
|
|
|
+ let omega, cosom, sinom, scale0, scale1;
|
|
|
+
|
|
|
+ // calc cosine
|
|
|
+ cosom = ax * bx + ay * by + az * bz + aw * bw;
|
|
|
+ // adjust signs (if necessary)
|
|
|
+ if ( cosom < 0.0 ) {
|
|
|
+ cosom = -cosom;
|
|
|
+ bx = - bx;
|
|
|
+ by = - by;
|
|
|
+ bz = - bz;
|
|
|
+ bw = - bw;
|
|
|
+ }
|
|
|
+ // calculate coefficients
|
|
|
+ if ( (1.0 - cosom) > 0.000001 ) {
|
|
|
+ // standard case (slerp)
|
|
|
+ omega = Math.acos(cosom);
|
|
|
+ sinom = Math.sin(omega);
|
|
|
+ scale0 = Math.sin((1.0 - t) * omega) / sinom;
|
|
|
+ scale1 = Math.sin(t * omega) / sinom;
|
|
|
+ } else {
|
|
|
+ // "from" and "to" quaternions are very close
|
|
|
+ // ... so we can do a linear interpolation
|
|
|
+ scale0 = 1.0 - t;
|
|
|
+ scale1 = t;
|
|
|
+ }
|
|
|
+ // calculate final values
|
|
|
+ out[0] = scale0 * ax + scale1 * bx;
|
|
|
+ out[1] = scale0 * ay + scale1 * by;
|
|
|
+ out[2] = scale0 * az + scale1 * bz;
|
|
|
+ out[3] = scale0 * aw + scale1 * bw;
|
|
|
+
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function invert(out: Quat, a: Quat) {
|
|
|
+ let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
|
|
|
+ let dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
|
|
|
+ let invDot = dot ? 1.0/dot : 0;
|
|
|
+
|
|
|
+ // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
|
|
|
+
|
|
|
+ out[0] = -a0 * invDot;
|
|
|
+ out[1] = -a1 * invDot;
|
|
|
+ out[2] = -a2 * invDot;
|
|
|
+ out[3] = a3 * invDot;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Calculates the conjugate of a quat
|
|
|
+ * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
|
|
|
+ */
|
|
|
+ export function conjugate(out: Quat, a: Quat) {
|
|
|
+ out[0] = -a[0];
|
|
|
+ out[1] = -a[1];
|
|
|
+ out[2] = -a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Creates a quaternion from the given 3x3 rotation matrix.
|
|
|
+ *
|
|
|
+ * NOTE: The resultant quaternion is not normalized, so you should be sure
|
|
|
+ * to renormalize the quaternion yourself where necessary.
|
|
|
+ */
|
|
|
+ export function fromMat3(out: Quat, m: Mat3) {
|
|
|
+ // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
|
|
|
+ // article "Quaternion Calculus and Fast Animation".
|
|
|
+ const fTrace = m[0] + m[4] + m[8];
|
|
|
+ let fRoot;
|
|
|
+
|
|
|
+ if ( fTrace > 0.0 ) {
|
|
|
+ // |w| > 1/2, may as well choose w > 1/2
|
|
|
+ fRoot = Math.sqrt(fTrace + 1.0); // 2w
|
|
|
+ out[3] = 0.5 * fRoot;
|
|
|
+ fRoot = 0.5/fRoot; // 1/(4w)
|
|
|
+ out[0] = (m[5]-m[7])*fRoot;
|
|
|
+ out[1] = (m[6]-m[2])*fRoot;
|
|
|
+ out[2] = (m[1]-m[3])*fRoot;
|
|
|
+ } else {
|
|
|
+ // |w| <= 1/2
|
|
|
+ let i = 0;
|
|
|
+ if ( m[4] > m[0] ) i = 1;
|
|
|
+ if ( m[8] > m[i*3+i] ) i = 2;
|
|
|
+ let j = (i+1)%3;
|
|
|
+ let k = (i+2)%3;
|
|
|
+
|
|
|
+ fRoot = Math.sqrt(m[i*3+i]-m[j*3+j]-m[k*3+k] + 1.0);
|
|
|
+ out[i] = 0.5 * fRoot;
|
|
|
+ fRoot = 0.5 / fRoot;
|
|
|
+ out[3] = (m[j*3+k] - m[k*3+j]) * fRoot;
|
|
|
+ out[j] = (m[j*3+i] + m[i*3+j]) * fRoot;
|
|
|
+ out[k] = (m[k*3+i] + m[i*3+k]) * fRoot;
|
|
|
+ }
|
|
|
+
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function clone(a: Quat) {
|
|
|
+ const out = zero();
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function copy(out: Quat, a: Quat) {
|
|
|
+ out[0] = a[0];
|
|
|
+ out[1] = a[1];
|
|
|
+ out[2] = a[2];
|
|
|
+ out[3] = a[3];
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function set(out: Quat, x: number, y: number, z: number, w: number) {
|
|
|
+ out[0] = x;
|
|
|
+ out[1] = y;
|
|
|
+ out[2] = z;
|
|
|
+ out[3] = w;
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function add(out: Quat, a: Quat, b: Quat) {
|
|
|
+ out[0] = a[0] + b[0];
|
|
|
+ out[1] = a[1] + b[1];
|
|
|
+ out[2] = a[2] + b[2];
|
|
|
+ out[3] = a[3] + b[3];
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function normalize(out: Quat, a: Quat) {
|
|
|
+ let x = a[0];
|
|
|
+ let y = a[1];
|
|
|
+ let z = a[2];
|
|
|
+ let w = a[3];
|
|
|
+ let len = x*x + y*y + z*z + w*w;
|
|
|
+ if (len > 0) {
|
|
|
+ len = 1 / Math.sqrt(len);
|
|
|
+ out[0] = x * len;
|
|
|
+ out[1] = y * len;
|
|
|
+ out[2] = z * len;
|
|
|
+ out[3] = w * len;
|
|
|
+ }
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Sets a quaternion to represent the shortest rotation from one
|
|
|
+ * vector to another.
|
|
|
+ *
|
|
|
+ * Both vectors are assumed to be unit length.
|
|
|
+ */
|
|
|
+ const rotTmpVec3 = Vec3.zero();
|
|
|
+ const rotTmpVec3UnitX = Vec3.create(1, 0, 0);
|
|
|
+ const rotTmpVec3UnitY = Vec3.create(0, 1, 0);
|
|
|
+ export function rotationTo(out: Quat, a: Vec3, b: Vec3) {
|
|
|
+ let dot = Vec3.dot(a, b);
|
|
|
+ if (dot < -0.999999) {
|
|
|
+ Vec3.cross(rotTmpVec3, rotTmpVec3UnitX, a);
|
|
|
+ if (Vec3.magnitude(rotTmpVec3) < 0.000001)
|
|
|
+ Vec3.cross(rotTmpVec3, rotTmpVec3UnitY, a);
|
|
|
+ Vec3.normalize(rotTmpVec3, rotTmpVec3);
|
|
|
+ setAxisAngle(out, rotTmpVec3, Math.PI);
|
|
|
+ return out;
|
|
|
+ } else if (dot > 0.999999) {
|
|
|
+ out[0] = 0;
|
|
|
+ out[1] = 0;
|
|
|
+ out[2] = 0;
|
|
|
+ out[3] = 1;
|
|
|
+ return out;
|
|
|
+ } else {
|
|
|
+ Vec3.cross(rotTmpVec3, a, b);
|
|
|
+ out[0] = rotTmpVec3[0];
|
|
|
+ out[1] = rotTmpVec3[1];
|
|
|
+ out[2] = rotTmpVec3[2];
|
|
|
+ out[3] = 1 + dot;
|
|
|
+ return normalize(out, out);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Performs a spherical linear interpolation with two control points
|
|
|
+ */
|
|
|
+ let sqlerpTemp1 = Quat.zero();
|
|
|
+ let sqlerpTemp2 = Quat.zero();
|
|
|
+ export function sqlerp(out: Quat, a: Quat, b: Quat, c: Quat, d: Quat, t: number) {
|
|
|
+ slerp(sqlerpTemp1, a, d, t);
|
|
|
+ slerp(sqlerpTemp2, b, c, t);
|
|
|
+ slerp(out, sqlerpTemp1, sqlerpTemp2, 2 * t * (1 - t));
|
|
|
+ return out;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Sets the specified quaternion with values corresponding to the given
|
|
|
+ * axes. Each axis is a vec3 and is expected to be unit length and
|
|
|
+ * perpendicular to all other specified axes.
|
|
|
+ */
|
|
|
+ const axesTmpMat = Mat3.zero();
|
|
|
+ export function setAxes(out: Quat, view: Vec3, right: Vec3, up: Vec3) {
|
|
|
+ axesTmpMat[0] = right[0];
|
|
|
+ axesTmpMat[3] = right[1];
|
|
|
+ axesTmpMat[6] = right[2];
|
|
|
+
|
|
|
+ axesTmpMat[1] = up[0];
|
|
|
+ axesTmpMat[4] = up[1];
|
|
|
+ axesTmpMat[7] = up[2];
|
|
|
+
|
|
|
+ axesTmpMat[2] = -view[0];
|
|
|
+ axesTmpMat[5] = -view[1];
|
|
|
+ axesTmpMat[8] = -view[2];
|
|
|
+
|
|
|
+ return normalize(out, Quat.fromMat3(out, axesTmpMat));
|
|
|
+ }
|
|
|
}
|