|
|
@@ -0,0 +1,1468 @@
|
|
|
+/*
|
|
|
+ * Copyright 2021 GFXFundamentals.
|
|
|
+ * All rights reserved.
|
|
|
+ *
|
|
|
+ * Redistribution and use in source and binary forms, with or without
|
|
|
+ * modification, are permitted provided that the following conditions are
|
|
|
+ * met:
|
|
|
+ *
|
|
|
+ * * Redistributions of source code must retain the above copyright
|
|
|
+ * notice, this list of conditions and the following disclaimer.
|
|
|
+ * * Redistributions in binary form must reproduce the above
|
|
|
+ * copyright notice, this list of conditions and the following disclaimer
|
|
|
+ * in the documentation and/or other materials provided with the
|
|
|
+ * distribution.
|
|
|
+ * * Neither the name of GFXFundamentals. nor the names of his
|
|
|
+ * contributors may be used to endorse or promote products derived from
|
|
|
+ * this software without specific prior written permission.
|
|
|
+ *
|
|
|
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
|
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
|
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
|
|
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
|
|
+ * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
|
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
|
|
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
|
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
|
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
|
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
|
|
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
|
+ */
|
|
|
+
|
|
|
+export namespace m4 {
|
|
|
+
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Various 3d math functions.
|
|
|
+ *
|
|
|
+ * @module webgl-3d-math
|
|
|
+ */
|
|
|
+
|
|
|
+ /**
|
|
|
+ * An array or typed array with 3 values.
|
|
|
+ * @typedef {number[]|TypedArray} Vector3
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+
|
|
|
+ /**
|
|
|
+ * An array or typed array with 4 values.
|
|
|
+ * @typedef {number[]|TypedArray} Vector4
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+
|
|
|
+ /**
|
|
|
+ * An array or typed array with 16 values.
|
|
|
+ * @typedef {number[]|TypedArray} Matrix4
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+
|
|
|
+
|
|
|
+ let MatType = Float32Array;
|
|
|
+ export type Matrix4 = Float32Array
|
|
|
+ export type Vector3 = Float32Array
|
|
|
+ export type Vector4 = Float32Array
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Sets the type this library creates for a Mat4
|
|
|
+ * @param {constructor} Ctor the constructor for the type. Either `Float32Array` or `Array`
|
|
|
+ * @return {constructor} previous constructor for Mat4
|
|
|
+ */
|
|
|
+ //function setDefaultType(Ctor) {
|
|
|
+ // const OldType = MatType;
|
|
|
+ // MatType = Ctor;
|
|
|
+ // return OldType;
|
|
|
+ //}
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Takes two 4-by-4 matrices, a and b, and computes the product in the order
|
|
|
+ * that pre-composes b with a. In other words, the matrix returned will
|
|
|
+ * transform by b first and then a. Note this is subtly different from just
|
|
|
+ * multiplying the matrices together. For given a and b, this function returns
|
|
|
+ * the same object in both row-major and column-major mode.
|
|
|
+ * @param {Matrix4} a A matrix.
|
|
|
+ * @param {Matrix4} b A matrix.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ */
|
|
|
+ export function multiply(a: Matrix4, b: Matrix4, dst: Matrix4 | null = null): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var b00 = b[0 * 4 + 0];
|
|
|
+ var b01 = b[0 * 4 + 1];
|
|
|
+ var b02 = b[0 * 4 + 2];
|
|
|
+ var b03 = b[0 * 4 + 3];
|
|
|
+ var b10 = b[1 * 4 + 0];
|
|
|
+ var b11 = b[1 * 4 + 1];
|
|
|
+ var b12 = b[1 * 4 + 2];
|
|
|
+ var b13 = b[1 * 4 + 3];
|
|
|
+ var b20 = b[2 * 4 + 0];
|
|
|
+ var b21 = b[2 * 4 + 1];
|
|
|
+ var b22 = b[2 * 4 + 2];
|
|
|
+ var b23 = b[2 * 4 + 3];
|
|
|
+ var b30 = b[3 * 4 + 0];
|
|
|
+ var b31 = b[3 * 4 + 1];
|
|
|
+ var b32 = b[3 * 4 + 2];
|
|
|
+ var b33 = b[3 * 4 + 3];
|
|
|
+ var a00 = a[0 * 4 + 0];
|
|
|
+ var a01 = a[0 * 4 + 1];
|
|
|
+ var a02 = a[0 * 4 + 2];
|
|
|
+ var a03 = a[0 * 4 + 3];
|
|
|
+ var a10 = a[1 * 4 + 0];
|
|
|
+ var a11 = a[1 * 4 + 1];
|
|
|
+ var a12 = a[1 * 4 + 2];
|
|
|
+ var a13 = a[1 * 4 + 3];
|
|
|
+ var a20 = a[2 * 4 + 0];
|
|
|
+ var a21 = a[2 * 4 + 1];
|
|
|
+ var a22 = a[2 * 4 + 2];
|
|
|
+ var a23 = a[2 * 4 + 3];
|
|
|
+ var a30 = a[3 * 4 + 0];
|
|
|
+ var a31 = a[3 * 4 + 1];
|
|
|
+ var a32 = a[3 * 4 + 2];
|
|
|
+ var a33 = a[3 * 4 + 3];
|
|
|
+ dst[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
|
|
|
+ dst[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
|
|
|
+ dst[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
|
|
|
+ dst[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
|
|
|
+ dst[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
|
|
|
+ dst[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
|
|
|
+ dst[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
|
|
|
+ dst[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
|
|
|
+ dst[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
|
|
|
+ dst[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
|
|
|
+ dst[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
|
|
|
+ dst[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
|
|
|
+ dst[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
|
|
|
+ dst[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
|
|
|
+ dst[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
|
|
|
+ dst[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ /**
|
|
|
+ * adds 2 vectors3s
|
|
|
+ * @param {Vector3} a a
|
|
|
+ * @param {Vector3} b b
|
|
|
+ * @param {Vector3} dst optional vector3 to store result
|
|
|
+ * @return {Vector3} dst or new Vector3 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function addVectors(a: Vector3, b: Vector3, dst: Vector3): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ dst[0] = a[0] + b[0];
|
|
|
+ dst[1] = a[1] + b[1];
|
|
|
+ dst[2] = a[2] + b[2];
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * subtracts 2 vectors3s
|
|
|
+ * @param {Vector3} a a
|
|
|
+ * @param {Vector3} b b
|
|
|
+ * @param {Vector3} dst optional vector3 to store result
|
|
|
+ * @return {Vector3} dst or new Vector3 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function subtractVectors(a: Vector3, b: Vector3, dst: Vector3 | null = null): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ dst[0] = a[0] - b[0];
|
|
|
+ dst[1] = a[1] - b[1];
|
|
|
+ dst[2] = a[2] - b[2];
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * scale vectors3
|
|
|
+ * @param {Vector3} v vector
|
|
|
+ * @param {Number} s scale
|
|
|
+ * @param {Vector3} dst optional vector3 to store result
|
|
|
+ * @return {Vector3} dst or new Vector3 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function scaleVector(v: Vector3, s: number, dst: Vector3): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ dst[0] = v[0] * s;
|
|
|
+ dst[1] = v[1] * s;
|
|
|
+ dst[2] = v[2] * s;
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * normalizes a vector.
|
|
|
+ * @param {Vector3} v vector to normalize
|
|
|
+ * @param {Vector3} dst optional vector3 to store result
|
|
|
+ * @return {Vector3} dst or new Vector3 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function normalize(v: Vector3, dst: Vector3 | null = null): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ var length = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
|
|
|
+ // make sure we don't divide by 0.
|
|
|
+ if (length > 0.00001) {
|
|
|
+ dst[0] = v[0] / length;
|
|
|
+ dst[1] = v[1] / length;
|
|
|
+ dst[2] = v[2] / length;
|
|
|
+ }
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the length of a vector
|
|
|
+ * @param {Vector3} v vector to take length of
|
|
|
+ * @return {number} length of vector
|
|
|
+ */
|
|
|
+ function length(v: Vector3): number {
|
|
|
+ return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the length squared of a vector
|
|
|
+ * @param {Vector3} v vector to take length of
|
|
|
+ * @return {number} length sqaured of vector
|
|
|
+ */
|
|
|
+ function lengthSq(v: Vector3): number {
|
|
|
+ return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the cross product of 2 vectors3s
|
|
|
+ * @param {Vector3} a a
|
|
|
+ * @param {Vector3} b b
|
|
|
+ * @param {Vector3} dst optional vector3 to store result
|
|
|
+ * @return {Vector3} dst or new Vector3 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function cross(a: Vector3, b: Vector3, dst: Vector3 | null = null): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ dst[0] = a[1] * b[2] - a[2] * b[1];
|
|
|
+ dst[1] = a[2] * b[0] - a[0] * b[2];
|
|
|
+ dst[2] = a[0] * b[1] - a[1] * b[0];
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the dot product of two vectors; assumes both vectors have
|
|
|
+ * three entries.
|
|
|
+ * @param {Vector3} a Operand vector.
|
|
|
+ * @param {Vector3} b Operand vector.
|
|
|
+ * @return {number} dot product
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function dot(a: Vector3, b: Vector3): number {
|
|
|
+ return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the distance squared between 2 points
|
|
|
+ * @param {Vector3} a
|
|
|
+ * @param {Vector3} b
|
|
|
+ * @return {number} distance squared between a and b
|
|
|
+ */
|
|
|
+ function distanceSq(a: Vector3, b: Vector3): number {
|
|
|
+ const dx = a[0] - b[0];
|
|
|
+ const dy = a[1] - b[1];
|
|
|
+ const dz = a[2] - b[2];
|
|
|
+ return dx * dx + dy * dy + dz * dz;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the distance between 2 points
|
|
|
+ * @param {Vector3} a
|
|
|
+ * @param {Vector3} b
|
|
|
+ * @return {number} distance between a and b
|
|
|
+ */
|
|
|
+ function distance(a: Vector3, b: Vector3): number {
|
|
|
+ return Math.sqrt(distanceSq(a, b));
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes an identity matrix.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function identity(dst: Matrix4 | null = null): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = 1;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = 1;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = 1;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Transposes a matrix.
|
|
|
+ * @param {Matrix4} m matrix to transpose.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function transpose(m: Matrix4, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = m[0];
|
|
|
+ dst[1] = m[4];
|
|
|
+ dst[2] = m[8];
|
|
|
+ dst[3] = m[12];
|
|
|
+ dst[4] = m[1];
|
|
|
+ dst[5] = m[5];
|
|
|
+ dst[6] = m[9];
|
|
|
+ dst[7] = m[13];
|
|
|
+ dst[8] = m[2];
|
|
|
+ dst[9] = m[6];
|
|
|
+ dst[10] = m[10];
|
|
|
+ dst[11] = m[14];
|
|
|
+ dst[12] = m[3];
|
|
|
+ dst[13] = m[7];
|
|
|
+ dst[14] = m[11];
|
|
|
+ dst[15] = m[15];
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Creates a lookAt matrix.
|
|
|
+ * This is a world matrix for a camera. In other words it will transform
|
|
|
+ * from the origin to a place and orientation in the world. For a view
|
|
|
+ * matrix take the inverse of this.
|
|
|
+ * @param {Vector3} cameraPosition position of the camera
|
|
|
+ * @param {Vector3} target position of the target
|
|
|
+ * @param {Vector3} up direction
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function lookAt(cameraPosition: Vector3, target: Vector3, up: Vector3, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var zAxis = normalize(
|
|
|
+ subtractVectors(cameraPosition, target));
|
|
|
+ var xAxis = normalize(cross(up, zAxis));
|
|
|
+ var yAxis = normalize(cross(zAxis, xAxis));
|
|
|
+
|
|
|
+ dst[0] = xAxis[0];
|
|
|
+ dst[1] = xAxis[1];
|
|
|
+ dst[2] = xAxis[2];
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = yAxis[0];
|
|
|
+ dst[5] = yAxis[1];
|
|
|
+ dst[6] = yAxis[2];
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = zAxis[0];
|
|
|
+ dst[9] = zAxis[1];
|
|
|
+ dst[10] = zAxis[2];
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = cameraPosition[0];
|
|
|
+ dst[13] = cameraPosition[1];
|
|
|
+ dst[14] = cameraPosition[2];
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes a 4-by-4 perspective transformation matrix given the angular height
|
|
|
+ * of the frustum, the aspect ratio, and the near and far clipping planes. The
|
|
|
+ * arguments define a frustum extending in the negative z direction. The given
|
|
|
+ * angle is the vertical angle of the frustum, and the horizontal angle is
|
|
|
+ * determined to produce the given aspect ratio. The arguments near and far are
|
|
|
+ * the distances to the near and far clipping planes. Note that near and far
|
|
|
+ * are not z coordinates, but rather they are distances along the negative
|
|
|
+ * z-axis. The matrix generated sends the viewing frustum to the unit box.
|
|
|
+ * We assume a unit box extending from -1 to 1 in the x and y dimensions and
|
|
|
+ * from -1 to 1 in the z dimension.
|
|
|
+ * @param {number} fieldOfViewInRadians field of view in y axis.
|
|
|
+ * @param {number} aspect aspect of viewport (width / height)
|
|
|
+ * @param {number} near near Z clipping plane
|
|
|
+ * @param {number} far far Z clipping plane
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function perspective(fieldOfViewInRadians: number, aspect: number, near: number, far: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewInRadians);
|
|
|
+ var rangeInv = 1.0 / (near - far);
|
|
|
+
|
|
|
+ dst[0] = f / aspect;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = f;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = (near + far) * rangeInv;
|
|
|
+ dst[11] = -1;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = near * far * rangeInv * 2;
|
|
|
+ dst[15] = 0;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes a 4-by-4 orthographic projection matrix given the coordinates of the
|
|
|
+ * planes defining the axis-aligned, box-shaped viewing volume. The matrix
|
|
|
+ * generated sends that box to the unit box. Note that although left and right
|
|
|
+ * are x coordinates and bottom and top are y coordinates, near and far
|
|
|
+ * are not z coordinates, but rather they are distances along the negative
|
|
|
+ * z-axis. We assume a unit box extending from -1 to 1 in the x and y
|
|
|
+ * dimensions and from -1 to 1 in the z dimension.
|
|
|
+ * @param {number} left The x coordinate of the left plane of the box.
|
|
|
+ * @param {number} right The x coordinate of the right plane of the box.
|
|
|
+ * @param {number} bottom The y coordinate of the bottom plane of the box.
|
|
|
+ * @param {number} top The y coordinate of the right plane of the box.
|
|
|
+ * @param {number} near The negative z coordinate of the near plane of the box.
|
|
|
+ * @param {number} far The negative z coordinate of the far plane of the box.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function orthographic(left: number, right: number, bottom: number, top: number, near: number, far: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = 2 / (right - left);
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = 2 / (top - bottom);
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = 2 / (near - far);
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = (left + right) / (left - right);
|
|
|
+ dst[13] = (bottom + top) / (bottom - top);
|
|
|
+ dst[14] = (near + far) / (near - far);
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes a 4-by-4 perspective transformation matrix given the left, right,
|
|
|
+ * top, bottom, near and far clipping planes. The arguments define a frustum
|
|
|
+ * extending in the negative z direction. The arguments near and far are the
|
|
|
+ * distances to the near and far clipping planes. Note that near and far are not
|
|
|
+ * z coordinates, but rather they are distances along the negative z-axis. The
|
|
|
+ * matrix generated sends the viewing frustum to the unit box. We assume a unit
|
|
|
+ * box extending from -1 to 1 in the x and y dimensions and from -1 to 1 in the z
|
|
|
+ * dimension.
|
|
|
+ * @param {number} left The x coordinate of the left plane of the box.
|
|
|
+ * @param {number} right The x coordinate of the right plane of the box.
|
|
|
+ * @param {number} bottom The y coordinate of the bottom plane of the box.
|
|
|
+ * @param {number} top The y coordinate of the right plane of the box.
|
|
|
+ * @param {number} near The negative z coordinate of the near plane of the box.
|
|
|
+ * @param {number} far The negative z coordinate of the far plane of the box.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var dx = right - left;
|
|
|
+ var dy = top - bottom;
|
|
|
+ var dz = far - near;
|
|
|
+
|
|
|
+ dst[0] = 2 * near / dx;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = 2 * near / dy;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = (left + right) / dx;
|
|
|
+ dst[9] = (top + bottom) / dy;
|
|
|
+ dst[10] = -(far + near) / dz;
|
|
|
+ dst[11] = -1;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = -2 * near * far / dz;
|
|
|
+ dst[15] = 0;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes a translation matrix
|
|
|
+ * @param {number} tx x translation.
|
|
|
+ * @param {number} ty y translation.
|
|
|
+ * @param {number} tz z translation.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function translation(tx: number, ty: number, tz: number, dst: Matrix4 | null = null): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = 1;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = 1;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = 1;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = tx;
|
|
|
+ dst[13] = ty;
|
|
|
+ dst[14] = tz;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by translation matrix.
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {number} tx x translation.
|
|
|
+ * @param {number} ty y translation.
|
|
|
+ * @param {number} tz z translation.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function translate(m: Matrix4, tx: number, ty: number, tz: number, dst: Matrix4): Matrix4 {
|
|
|
+ // This is the optimized version of
|
|
|
+ // return multiply(m, translation(tx, ty, tz), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var m00 = m[0];
|
|
|
+ var m01 = m[1];
|
|
|
+ var m02 = m[2];
|
|
|
+ var m03 = m[3];
|
|
|
+ var m10 = m[1 * 4 + 0];
|
|
|
+ var m11 = m[1 * 4 + 1];
|
|
|
+ var m12 = m[1 * 4 + 2];
|
|
|
+ var m13 = m[1 * 4 + 3];
|
|
|
+ var m20 = m[2 * 4 + 0];
|
|
|
+ var m21 = m[2 * 4 + 1];
|
|
|
+ var m22 = m[2 * 4 + 2];
|
|
|
+ var m23 = m[2 * 4 + 3];
|
|
|
+ var m30 = m[3 * 4 + 0];
|
|
|
+ var m31 = m[3 * 4 + 1];
|
|
|
+ var m32 = m[3 * 4 + 2];
|
|
|
+ var m33 = m[3 * 4 + 3];
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[0] = m00;
|
|
|
+ dst[1] = m01;
|
|
|
+ dst[2] = m02;
|
|
|
+ dst[3] = m03;
|
|
|
+ dst[4] = m10;
|
|
|
+ dst[5] = m11;
|
|
|
+ dst[6] = m12;
|
|
|
+ dst[7] = m13;
|
|
|
+ dst[8] = m20;
|
|
|
+ dst[9] = m21;
|
|
|
+ dst[10] = m22;
|
|
|
+ dst[11] = m23;
|
|
|
+ }
|
|
|
+
|
|
|
+ dst[12] = m00 * tx + m10 * ty + m20 * tz + m30;
|
|
|
+ dst[13] = m01 * tx + m11 * ty + m21 * tz + m31;
|
|
|
+ dst[14] = m02 * tx + m12 * ty + m22 * tz + m32;
|
|
|
+ dst[15] = m03 * tx + m13 * ty + m23 * tz + m33;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes an x rotation matrix
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function xRotation(angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[0] = 1;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = c;
|
|
|
+ dst[6] = s;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = -s;
|
|
|
+ dst[10] = c;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by an x rotation matrix
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function xRotate(m: Matrix4, angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ // this is the optimized version of
|
|
|
+ // return multiply(m, xRotation(angleInRadians), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var m10 = m[4];
|
|
|
+ var m11 = m[5];
|
|
|
+ var m12 = m[6];
|
|
|
+ var m13 = m[7];
|
|
|
+ var m20 = m[8];
|
|
|
+ var m21 = m[9];
|
|
|
+ var m22 = m[10];
|
|
|
+ var m23 = m[11];
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[4] = c * m10 + s * m20;
|
|
|
+ dst[5] = c * m11 + s * m21;
|
|
|
+ dst[6] = c * m12 + s * m22;
|
|
|
+ dst[7] = c * m13 + s * m23;
|
|
|
+ dst[8] = c * m20 - s * m10;
|
|
|
+ dst[9] = c * m21 - s * m11;
|
|
|
+ dst[10] = c * m22 - s * m12;
|
|
|
+ dst[11] = c * m23 - s * m13;
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[0] = m[0];
|
|
|
+ dst[1] = m[1];
|
|
|
+ dst[2] = m[2];
|
|
|
+ dst[3] = m[3];
|
|
|
+ dst[12] = m[12];
|
|
|
+ dst[13] = m[13];
|
|
|
+ dst[14] = m[14];
|
|
|
+ dst[15] = m[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes an y rotation matrix
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function yRotation(angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[0] = c;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = -s;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = 1;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = s;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = c;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by an y rotation matrix
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function yRotate(m: Matrix4, angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ // this is the optimized version of
|
|
|
+ // return multiply(m, yRotation(angleInRadians), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var m00 = m[0 * 4 + 0];
|
|
|
+ var m01 = m[0 * 4 + 1];
|
|
|
+ var m02 = m[0 * 4 + 2];
|
|
|
+ var m03 = m[0 * 4 + 3];
|
|
|
+ var m20 = m[2 * 4 + 0];
|
|
|
+ var m21 = m[2 * 4 + 1];
|
|
|
+ var m22 = m[2 * 4 + 2];
|
|
|
+ var m23 = m[2 * 4 + 3];
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[0] = c * m00 - s * m20;
|
|
|
+ dst[1] = c * m01 - s * m21;
|
|
|
+ dst[2] = c * m02 - s * m22;
|
|
|
+ dst[3] = c * m03 - s * m23;
|
|
|
+ dst[8] = c * m20 + s * m00;
|
|
|
+ dst[9] = c * m21 + s * m01;
|
|
|
+ dst[10] = c * m22 + s * m02;
|
|
|
+ dst[11] = c * m23 + s * m03;
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[4] = m[4];
|
|
|
+ dst[5] = m[5];
|
|
|
+ dst[6] = m[6];
|
|
|
+ dst[7] = m[7];
|
|
|
+ dst[12] = m[12];
|
|
|
+ dst[13] = m[13];
|
|
|
+ dst[14] = m[14];
|
|
|
+ dst[15] = m[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes an z rotation matrix
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function zRotation(angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[0] = c;
|
|
|
+ dst[1] = s;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = -s;
|
|
|
+ dst[5] = c;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = 1;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by an z rotation matrix
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function zRotate(m: Matrix4, angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ // This is the optimized version of
|
|
|
+ // return multiply(m, zRotation(angleInRadians), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var m00 = m[0 * 4 + 0];
|
|
|
+ var m01 = m[0 * 4 + 1];
|
|
|
+ var m02 = m[0 * 4 + 2];
|
|
|
+ var m03 = m[0 * 4 + 3];
|
|
|
+ var m10 = m[1 * 4 + 0];
|
|
|
+ var m11 = m[1 * 4 + 1];
|
|
|
+ var m12 = m[1 * 4 + 2];
|
|
|
+ var m13 = m[1 * 4 + 3];
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+
|
|
|
+ dst[0] = c * m00 + s * m10;
|
|
|
+ dst[1] = c * m01 + s * m11;
|
|
|
+ dst[2] = c * m02 + s * m12;
|
|
|
+ dst[3] = c * m03 + s * m13;
|
|
|
+ dst[4] = c * m10 - s * m00;
|
|
|
+ dst[5] = c * m11 - s * m01;
|
|
|
+ dst[6] = c * m12 - s * m02;
|
|
|
+ dst[7] = c * m13 - s * m03;
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[8] = m[8];
|
|
|
+ dst[9] = m[9];
|
|
|
+ dst[10] = m[10];
|
|
|
+ dst[11] = m[11];
|
|
|
+ dst[12] = m[12];
|
|
|
+ dst[13] = m[13];
|
|
|
+ dst[14] = m[14];
|
|
|
+ dst[15] = m[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes an rotation matrix around an arbitrary axis
|
|
|
+ * @param {Vector3} axis axis to rotate around
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function axisRotation(axis: Vector3, angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var x = axis[0];
|
|
|
+ var y = axis[1];
|
|
|
+ var z = axis[2];
|
|
|
+ var n = Math.sqrt(x * x + y * y + z * z);
|
|
|
+ x /= n;
|
|
|
+ y /= n;
|
|
|
+ z /= n;
|
|
|
+ var xx = x * x;
|
|
|
+ var yy = y * y;
|
|
|
+ var zz = z * z;
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+ var oneMinusCosine = 1 - c;
|
|
|
+
|
|
|
+ dst[0] = xx + (1 - xx) * c;
|
|
|
+ dst[1] = x * y * oneMinusCosine + z * s;
|
|
|
+ dst[2] = x * z * oneMinusCosine - y * s;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = x * y * oneMinusCosine - z * s;
|
|
|
+ dst[5] = yy + (1 - yy) * c;
|
|
|
+ dst[6] = y * z * oneMinusCosine + x * s;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = x * z * oneMinusCosine + y * s;
|
|
|
+ dst[9] = y * z * oneMinusCosine - x * s;
|
|
|
+ dst[10] = zz + (1 - zz) * c;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by an axis rotation matrix
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {Vector3} axis axis to rotate around
|
|
|
+ * @param {number} angleInRadians amount to rotate
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function axisRotate(m: Matrix4, axis: Vector3, angleInRadians: number, dst: Matrix4): Matrix4 {
|
|
|
+ // This is the optimized version of
|
|
|
+ // return multiply(m, axisRotation(axis, angleInRadians), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ var x = axis[0];
|
|
|
+ var y = axis[1];
|
|
|
+ var z = axis[2];
|
|
|
+ var n = Math.sqrt(x * x + y * y + z * z);
|
|
|
+ x /= n;
|
|
|
+ y /= n;
|
|
|
+ z /= n;
|
|
|
+ var xx = x * x;
|
|
|
+ var yy = y * y;
|
|
|
+ var zz = z * z;
|
|
|
+ var c = Math.cos(angleInRadians);
|
|
|
+ var s = Math.sin(angleInRadians);
|
|
|
+ var oneMinusCosine = 1 - c;
|
|
|
+
|
|
|
+ var r00 = xx + (1 - xx) * c;
|
|
|
+ var r01 = x * y * oneMinusCosine + z * s;
|
|
|
+ var r02 = x * z * oneMinusCosine - y * s;
|
|
|
+ var r10 = x * y * oneMinusCosine - z * s;
|
|
|
+ var r11 = yy + (1 - yy) * c;
|
|
|
+ var r12 = y * z * oneMinusCosine + x * s;
|
|
|
+ var r20 = x * z * oneMinusCosine + y * s;
|
|
|
+ var r21 = y * z * oneMinusCosine - x * s;
|
|
|
+ var r22 = zz + (1 - zz) * c;
|
|
|
+
|
|
|
+ var m00 = m[0];
|
|
|
+ var m01 = m[1];
|
|
|
+ var m02 = m[2];
|
|
|
+ var m03 = m[3];
|
|
|
+ var m10 = m[4];
|
|
|
+ var m11 = m[5];
|
|
|
+ var m12 = m[6];
|
|
|
+ var m13 = m[7];
|
|
|
+ var m20 = m[8];
|
|
|
+ var m21 = m[9];
|
|
|
+ var m22 = m[10];
|
|
|
+ var m23 = m[11];
|
|
|
+
|
|
|
+ dst[0] = r00 * m00 + r01 * m10 + r02 * m20;
|
|
|
+ dst[1] = r00 * m01 + r01 * m11 + r02 * m21;
|
|
|
+ dst[2] = r00 * m02 + r01 * m12 + r02 * m22;
|
|
|
+ dst[3] = r00 * m03 + r01 * m13 + r02 * m23;
|
|
|
+ dst[4] = r10 * m00 + r11 * m10 + r12 * m20;
|
|
|
+ dst[5] = r10 * m01 + r11 * m11 + r12 * m21;
|
|
|
+ dst[6] = r10 * m02 + r11 * m12 + r12 * m22;
|
|
|
+ dst[7] = r10 * m03 + r11 * m13 + r12 * m23;
|
|
|
+ dst[8] = r20 * m00 + r21 * m10 + r22 * m20;
|
|
|
+ dst[9] = r20 * m01 + r21 * m11 + r22 * m21;
|
|
|
+ dst[10] = r20 * m02 + r21 * m12 + r22 * m22;
|
|
|
+ dst[11] = r20 * m03 + r21 * m13 + r22 * m23;
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[12] = m[12];
|
|
|
+ dst[13] = m[13];
|
|
|
+ dst[14] = m[14];
|
|
|
+ dst[15] = m[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Makes a scale matrix
|
|
|
+ * @param {number} sx x scale.
|
|
|
+ * @param {number} sy y scale.
|
|
|
+ * @param {number} sz z scale.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function scaling(sx: number, sy: number, sz: number, dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = sx;
|
|
|
+ dst[1] = 0;
|
|
|
+ dst[2] = 0;
|
|
|
+ dst[3] = 0;
|
|
|
+ dst[4] = 0;
|
|
|
+ dst[5] = sy;
|
|
|
+ dst[6] = 0;
|
|
|
+ dst[7] = 0;
|
|
|
+ dst[8] = 0;
|
|
|
+ dst[9] = 0;
|
|
|
+ dst[10] = sz;
|
|
|
+ dst[11] = 0;
|
|
|
+ dst[12] = 0;
|
|
|
+ dst[13] = 0;
|
|
|
+ dst[14] = 0;
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Multiply by a scaling matrix
|
|
|
+ * @param {Matrix4} m matrix to multiply
|
|
|
+ * @param {number} sx x scale.
|
|
|
+ * @param {number} sy y scale.
|
|
|
+ * @param {number} sz z scale.
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function scale(m: Matrix4, sx: number, sy: number, sz: number, dst: Matrix4): Matrix4 {
|
|
|
+ // This is the optimized version of
|
|
|
+ // return multiply(m, scaling(sx, sy, sz), dst);
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = sx * m[0 * 4 + 0];
|
|
|
+ dst[1] = sx * m[0 * 4 + 1];
|
|
|
+ dst[2] = sx * m[0 * 4 + 2];
|
|
|
+ dst[3] = sx * m[0 * 4 + 3];
|
|
|
+ dst[4] = sy * m[1 * 4 + 0];
|
|
|
+ dst[5] = sy * m[1 * 4 + 1];
|
|
|
+ dst[6] = sy * m[1 * 4 + 2];
|
|
|
+ dst[7] = sy * m[1 * 4 + 3];
|
|
|
+ dst[8] = sz * m[2 * 4 + 0];
|
|
|
+ dst[9] = sz * m[2 * 4 + 1];
|
|
|
+ dst[10] = sz * m[2 * 4 + 2];
|
|
|
+ dst[11] = sz * m[2 * 4 + 3];
|
|
|
+
|
|
|
+ if (m !== dst) {
|
|
|
+ dst[12] = m[12];
|
|
|
+ dst[13] = m[13];
|
|
|
+ dst[14] = m[14];
|
|
|
+ dst[15] = m[15];
|
|
|
+ }
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * creates a matrix from translation, quaternion, scale
|
|
|
+ * @param {Number[]} translation [x, y, z] translation
|
|
|
+ * @param {Number[]} quaternion [x, y, z, z] quaternion rotation
|
|
|
+ * @param {Number[]} scale [x, y, z] scale
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ */
|
|
|
+ function compose(translation: number[], quaternion: number[], scale: number[], dst: Matrix4): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ const x = quaternion[0];
|
|
|
+ const y = quaternion[1];
|
|
|
+ const z = quaternion[2];
|
|
|
+ const w = quaternion[3];
|
|
|
+
|
|
|
+ const x2 = x + x;
|
|
|
+ const y2 = y + y;
|
|
|
+ const z2 = z + z;
|
|
|
+
|
|
|
+ const xx = x * x2;
|
|
|
+ const xy = x * y2;
|
|
|
+ const xz = x * z2;
|
|
|
+
|
|
|
+ const yy = y * y2;
|
|
|
+ const yz = y * z2;
|
|
|
+ const zz = z * z2;
|
|
|
+
|
|
|
+ const wx = w * x2;
|
|
|
+ const wy = w * y2;
|
|
|
+ const wz = w * z2;
|
|
|
+
|
|
|
+ const sx = scale[0];
|
|
|
+ const sy = scale[1];
|
|
|
+ const sz = scale[2];
|
|
|
+
|
|
|
+ dst[0] = (1 - (yy + zz)) * sx;
|
|
|
+ dst[1] = (xy + wz) * sx;
|
|
|
+ dst[2] = (xz - wy) * sx;
|
|
|
+ dst[3] = 0;
|
|
|
+
|
|
|
+ dst[4] = (xy - wz) * sy;
|
|
|
+ dst[5] = (1 - (xx + zz)) * sy;
|
|
|
+ dst[6] = (yz + wx) * sy;
|
|
|
+ dst[7] = 0;
|
|
|
+
|
|
|
+ dst[8] = (xz + wy) * sz;
|
|
|
+ dst[9] = (yz - wx) * sz;
|
|
|
+ dst[10] = (1 - (xx + yy)) * sz;
|
|
|
+ dst[11] = 0;
|
|
|
+
|
|
|
+ dst[12] = translation[0];
|
|
|
+ dst[13] = translation[1];
|
|
|
+ dst[14] = translation[2];
|
|
|
+ dst[15] = 1;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ function quatFromRotationMatrix(m: Matrix4, dst: Matrix4) {
|
|
|
+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
|
|
|
+
|
|
|
+ // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
|
|
|
+ const m11 = m[0];
|
|
|
+ const m12 = m[4];
|
|
|
+ const m13 = m[8];
|
|
|
+ const m21 = m[1];
|
|
|
+ const m22 = m[5];
|
|
|
+ const m23 = m[9];
|
|
|
+ const m31 = m[2];
|
|
|
+ const m32 = m[6];
|
|
|
+ const m33 = m[10];
|
|
|
+
|
|
|
+ const trace = m11 + m22 + m33;
|
|
|
+
|
|
|
+ if (trace > 0) {
|
|
|
+ const s = 0.5 / Math.sqrt(trace + 1);
|
|
|
+ dst[3] = 0.25 / s;
|
|
|
+ dst[0] = (m32 - m23) * s;
|
|
|
+ dst[1] = (m13 - m31) * s;
|
|
|
+ dst[2] = (m21 - m12) * s;
|
|
|
+ } else if (m11 > m22 && m11 > m33) {
|
|
|
+ const s = 2 * Math.sqrt(1 + m11 - m22 - m33);
|
|
|
+ dst[3] = (m32 - m23) / s;
|
|
|
+ dst[0] = 0.25 * s;
|
|
|
+ dst[1] = (m12 + m21) / s;
|
|
|
+ dst[2] = (m13 + m31) / s;
|
|
|
+ } else if (m22 > m33) {
|
|
|
+ const s = 2 * Math.sqrt(1 + m22 - m11 - m33);
|
|
|
+ dst[3] = (m13 - m31) / s;
|
|
|
+ dst[0] = (m12 + m21) / s;
|
|
|
+ dst[1] = 0.25 * s;
|
|
|
+ dst[2] = (m23 + m32) / s;
|
|
|
+ } else {
|
|
|
+ const s = 2 * Math.sqrt(1 + m33 - m11 - m22);
|
|
|
+ dst[3] = (m21 - m12) / s;
|
|
|
+ dst[0] = (m13 + m31) / s;
|
|
|
+ dst[1] = (m23 + m32) / s;
|
|
|
+ dst[2] = 0.25 * s;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ function decompose(mat: Matrix4, translation: Matrix4, quaternion: Matrix4, scale: Matrix4) {
|
|
|
+ let sx = length(mat.slice(0, 3));
|
|
|
+ const sy = length(mat.slice(4, 7));
|
|
|
+ const sz = length(mat.slice(8, 11));
|
|
|
+
|
|
|
+ // if determinate is negative, we need to invert one scale
|
|
|
+ const det = determinate(mat);
|
|
|
+ if (det < 0) {
|
|
|
+ sx = -sx;
|
|
|
+ }
|
|
|
+
|
|
|
+ translation[0] = mat[12];
|
|
|
+ translation[1] = mat[13];
|
|
|
+ translation[2] = mat[14];
|
|
|
+
|
|
|
+ // scale the rotation part
|
|
|
+ const matrix = copy(mat);
|
|
|
+
|
|
|
+ const invSX = 1 / sx;
|
|
|
+ const invSY = 1 / sy;
|
|
|
+ const invSZ = 1 / sz;
|
|
|
+
|
|
|
+ matrix[0] *= invSX;
|
|
|
+ matrix[1] *= invSX;
|
|
|
+ matrix[2] *= invSX;
|
|
|
+
|
|
|
+ matrix[4] *= invSY;
|
|
|
+ matrix[5] *= invSY;
|
|
|
+ matrix[6] *= invSY;
|
|
|
+
|
|
|
+ matrix[8] *= invSZ;
|
|
|
+ matrix[9] *= invSZ;
|
|
|
+ matrix[10] *= invSZ;
|
|
|
+
|
|
|
+ quatFromRotationMatrix(matrix, quaternion);
|
|
|
+
|
|
|
+ scale[0] = sx;
|
|
|
+ scale[1] = sy;
|
|
|
+ scale[2] = sz;
|
|
|
+ }
|
|
|
+
|
|
|
+ function determinate(m: Matrix4): number {
|
|
|
+ var m00 = m[0 * 4 + 0];
|
|
|
+ var m01 = m[0 * 4 + 1];
|
|
|
+ var m02 = m[0 * 4 + 2];
|
|
|
+ var m03 = m[0 * 4 + 3];
|
|
|
+ var m10 = m[1 * 4 + 0];
|
|
|
+ var m11 = m[1 * 4 + 1];
|
|
|
+ var m12 = m[1 * 4 + 2];
|
|
|
+ var m13 = m[1 * 4 + 3];
|
|
|
+ var m20 = m[2 * 4 + 0];
|
|
|
+ var m21 = m[2 * 4 + 1];
|
|
|
+ var m22 = m[2 * 4 + 2];
|
|
|
+ var m23 = m[2 * 4 + 3];
|
|
|
+ var m30 = m[3 * 4 + 0];
|
|
|
+ var m31 = m[3 * 4 + 1];
|
|
|
+ var m32 = m[3 * 4 + 2];
|
|
|
+ var m33 = m[3 * 4 + 3];
|
|
|
+ var tmp_0 = m22 * m33;
|
|
|
+ var tmp_1 = m32 * m23;
|
|
|
+ var tmp_2 = m12 * m33;
|
|
|
+ var tmp_3 = m32 * m13;
|
|
|
+ var tmp_4 = m12 * m23;
|
|
|
+ var tmp_5 = m22 * m13;
|
|
|
+ var tmp_6 = m02 * m33;
|
|
|
+ var tmp_7 = m32 * m03;
|
|
|
+ var tmp_8 = m02 * m23;
|
|
|
+ var tmp_9 = m22 * m03;
|
|
|
+ var tmp_10 = m02 * m13;
|
|
|
+ var tmp_11 = m12 * m03;
|
|
|
+
|
|
|
+ var t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -
|
|
|
+ (tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
|
|
|
+ var t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -
|
|
|
+ (tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
|
|
|
+ var t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -
|
|
|
+ (tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
|
|
|
+ var t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -
|
|
|
+ (tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);
|
|
|
+
|
|
|
+ return 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Computes the inverse of a matrix.
|
|
|
+ * @param {Matrix4} m matrix to compute inverse of
|
|
|
+ * @param {Matrix4} [dst] optional matrix to store result
|
|
|
+ * @return {Matrix4} dst or a new matrix if none provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function inverse(m: Matrix4, dst: Matrix4 | null = null): Matrix4 {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+ var m00 = m[0 * 4 + 0];
|
|
|
+ var m01 = m[0 * 4 + 1];
|
|
|
+ var m02 = m[0 * 4 + 2];
|
|
|
+ var m03 = m[0 * 4 + 3];
|
|
|
+ var m10 = m[1 * 4 + 0];
|
|
|
+ var m11 = m[1 * 4 + 1];
|
|
|
+ var m12 = m[1 * 4 + 2];
|
|
|
+ var m13 = m[1 * 4 + 3];
|
|
|
+ var m20 = m[2 * 4 + 0];
|
|
|
+ var m21 = m[2 * 4 + 1];
|
|
|
+ var m22 = m[2 * 4 + 2];
|
|
|
+ var m23 = m[2 * 4 + 3];
|
|
|
+ var m30 = m[3 * 4 + 0];
|
|
|
+ var m31 = m[3 * 4 + 1];
|
|
|
+ var m32 = m[3 * 4 + 2];
|
|
|
+ var m33 = m[3 * 4 + 3];
|
|
|
+ var tmp_0 = m22 * m33;
|
|
|
+ var tmp_1 = m32 * m23;
|
|
|
+ var tmp_2 = m12 * m33;
|
|
|
+ var tmp_3 = m32 * m13;
|
|
|
+ var tmp_4 = m12 * m23;
|
|
|
+ var tmp_5 = m22 * m13;
|
|
|
+ var tmp_6 = m02 * m33;
|
|
|
+ var tmp_7 = m32 * m03;
|
|
|
+ var tmp_8 = m02 * m23;
|
|
|
+ var tmp_9 = m22 * m03;
|
|
|
+ var tmp_10 = m02 * m13;
|
|
|
+ var tmp_11 = m12 * m03;
|
|
|
+ var tmp_12 = m20 * m31;
|
|
|
+ var tmp_13 = m30 * m21;
|
|
|
+ var tmp_14 = m10 * m31;
|
|
|
+ var tmp_15 = m30 * m11;
|
|
|
+ var tmp_16 = m10 * m21;
|
|
|
+ var tmp_17 = m20 * m11;
|
|
|
+ var tmp_18 = m00 * m31;
|
|
|
+ var tmp_19 = m30 * m01;
|
|
|
+ var tmp_20 = m00 * m21;
|
|
|
+ var tmp_21 = m20 * m01;
|
|
|
+ var tmp_22 = m00 * m11;
|
|
|
+ var tmp_23 = m10 * m01;
|
|
|
+
|
|
|
+ var t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -
|
|
|
+ (tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
|
|
|
+ var t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -
|
|
|
+ (tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
|
|
|
+ var t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -
|
|
|
+ (tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
|
|
|
+ var t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -
|
|
|
+ (tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);
|
|
|
+
|
|
|
+ var d = 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);
|
|
|
+
|
|
|
+ dst[0] = d * t0;
|
|
|
+ dst[1] = d * t1;
|
|
|
+ dst[2] = d * t2;
|
|
|
+ dst[3] = d * t3;
|
|
|
+ dst[4] = d * ((tmp_1 * m10 + tmp_2 * m20 + tmp_5 * m30) -
|
|
|
+ (tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30));
|
|
|
+ dst[5] = d * ((tmp_0 * m00 + tmp_7 * m20 + tmp_8 * m30) -
|
|
|
+ (tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30));
|
|
|
+ dst[6] = d * ((tmp_3 * m00 + tmp_6 * m10 + tmp_11 * m30) -
|
|
|
+ (tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30));
|
|
|
+ dst[7] = d * ((tmp_4 * m00 + tmp_9 * m10 + tmp_10 * m20) -
|
|
|
+ (tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20));
|
|
|
+ dst[8] = d * ((tmp_12 * m13 + tmp_15 * m23 + tmp_16 * m33) -
|
|
|
+ (tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33));
|
|
|
+ dst[9] = d * ((tmp_13 * m03 + tmp_18 * m23 + tmp_21 * m33) -
|
|
|
+ (tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33));
|
|
|
+ dst[10] = d * ((tmp_14 * m03 + tmp_19 * m13 + tmp_22 * m33) -
|
|
|
+ (tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33));
|
|
|
+ dst[11] = d * ((tmp_17 * m03 + tmp_20 * m13 + tmp_23 * m23) -
|
|
|
+ (tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23));
|
|
|
+ dst[12] = d * ((tmp_14 * m22 + tmp_17 * m32 + tmp_13 * m12) -
|
|
|
+ (tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22));
|
|
|
+ dst[13] = d * ((tmp_20 * m32 + tmp_12 * m02 + tmp_19 * m22) -
|
|
|
+ (tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02));
|
|
|
+ dst[14] = d * ((tmp_18 * m12 + tmp_23 * m32 + tmp_15 * m02) -
|
|
|
+ (tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12));
|
|
|
+ dst[15] = d * ((tmp_22 * m22 + tmp_16 * m02 + tmp_21 * m12) -
|
|
|
+ (tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02));
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Takes a matrix and a vector with 4 entries, transforms that vector by
|
|
|
+ * the matrix, and returns the result as a vector with 4 entries.
|
|
|
+ * @param {Matrix4} m The matrix.
|
|
|
+ * @param {Vector4} v The point in homogenous coordinates.
|
|
|
+ * @param {Vector4} dst optional vector4 to store result
|
|
|
+ * @return {Vector4} dst or new Vector4 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function transformVector(m: Matrix4, v: Vector4, dst: Vector4): Vector4 {
|
|
|
+ dst = dst || new MatType(4);
|
|
|
+ for (var i = 0; i < 4; ++i) {
|
|
|
+ dst[i] = 0.0;
|
|
|
+ for (var j = 0; j < 4; ++j) {
|
|
|
+ dst[i] += v[j] * m[j * 4 + i];
|
|
|
+ }
|
|
|
+ }
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Takes a 4-by-4 matrix and a vector with 3 entries,
|
|
|
+ * interprets the vector as a point, transforms that point by the matrix, and
|
|
|
+ * returns the result as a vector with 3 entries.
|
|
|
+ * @param {Matrix4} m The matrix.
|
|
|
+ * @param {Vector3} v The point.
|
|
|
+ * @param {Vector4} dst optional vector4 to store result
|
|
|
+ * @return {Vector4} dst or new Vector4 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ export function transformPoint(m: Matrix4, v: Vector3, dst: Vector4 | null = null): Vector4 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ var v0 = v[0];
|
|
|
+ var v1 = v[1];
|
|
|
+ var v2 = v[2];
|
|
|
+ var d = v0 * m[0 * 4 + 3] + v1 * m[1 * 4 + 3] + v2 * m[2 * 4 + 3] + m[3 * 4 + 3];
|
|
|
+
|
|
|
+ dst[0] = (v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0] + m[3 * 4 + 0]) / d;
|
|
|
+ dst[1] = (v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1] + m[3 * 4 + 1]) / d;
|
|
|
+ dst[2] = (v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2] + m[3 * 4 + 2]) / d;
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Takes a 4-by-4 matrix and a vector with 3 entries, interprets the vector as a
|
|
|
+ * direction, transforms that direction by the matrix, and returns the result;
|
|
|
+ * assumes the transformation of 3-dimensional space represented by the matrix
|
|
|
+ * is parallel-preserving, i.e. any combination of rotation, scaling and
|
|
|
+ * translation, but not a perspective distortion. Returns a vector with 3
|
|
|
+ * entries.
|
|
|
+ * @param {Matrix4} m The matrix.
|
|
|
+ * @param {Vector3} v The direction.
|
|
|
+ * @param {Vector4} dst optional vector4 to store result
|
|
|
+ * @return {Vector4} dst or new Vector4 if not provided
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function transformDirection(m: Matrix4, v: Vector3, dst: Vector4): Vector4 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+
|
|
|
+ var v0 = v[0];
|
|
|
+ var v1 = v[1];
|
|
|
+ var v2 = v[2];
|
|
|
+
|
|
|
+ dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];
|
|
|
+ dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];
|
|
|
+ dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ /**
|
|
|
+ * Takes a 4-by-4 matrix m and a vector v with 3 entries, interprets the vector
|
|
|
+ * as a normal to a surface, and computes a vector which is normal upon
|
|
|
+ * transforming that surface by the matrix. The effect of this function is the
|
|
|
+ * same as transforming v (as a direction) by the inverse-transpose of m. This
|
|
|
+ * function assumes the transformation of 3-dimensional space represented by the
|
|
|
+ * matrix is parallel-preserving, i.e. any combination of rotation, scaling and
|
|
|
+ * translation, but not a perspective distortion. Returns a vector with 3
|
|
|
+ * entries.
|
|
|
+ * @param {Matrix4} m The matrix.
|
|
|
+ * @param {Vector3} v The normal.
|
|
|
+ * @param {Vector3} [dst] The direction.
|
|
|
+ * @return {Vector3} The transformed direction.
|
|
|
+ * @memberOf module:webgl-3d-math
|
|
|
+ */
|
|
|
+ function transformNormal(m: Matrix4, v: Vector3, dst: Vector3): Vector3 {
|
|
|
+ dst = dst || new MatType(3);
|
|
|
+ var mi = inverse(m);
|
|
|
+ var v0 = v[0];
|
|
|
+ var v1 = v[1];
|
|
|
+ var v2 = v[2];
|
|
|
+
|
|
|
+ dst[0] = v0 * mi[0 * 4 + 0] + v1 * mi[0 * 4 + 1] + v2 * mi[0 * 4 + 2];
|
|
|
+ dst[1] = v0 * mi[1 * 4 + 0] + v1 * mi[1 * 4 + 1] + v2 * mi[1 * 4 + 2];
|
|
|
+ dst[2] = v0 * mi[2 * 4 + 0] + v1 * mi[2 * 4 + 1] + v2 * mi[2 * 4 + 2];
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+ export function copy(src: Matrix4, dst: Matrix4 | null = null) {
|
|
|
+ dst = dst || new MatType(16);
|
|
|
+
|
|
|
+ dst[0] = src[0];
|
|
|
+ dst[1] = src[1];
|
|
|
+ dst[2] = src[2];
|
|
|
+ dst[3] = src[3];
|
|
|
+ dst[4] = src[4];
|
|
|
+ dst[5] = src[5];
|
|
|
+ dst[6] = src[6];
|
|
|
+ dst[7] = src[7];
|
|
|
+ dst[8] = src[8];
|
|
|
+ dst[9] = src[9];
|
|
|
+ dst[10] = src[10];
|
|
|
+ dst[11] = src[11];
|
|
|
+ dst[12] = src[12];
|
|
|
+ dst[13] = src[13];
|
|
|
+ dst[14] = src[14];
|
|
|
+ dst[15] = src[15];
|
|
|
+
|
|
|
+ return dst;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+ export function projection( width: number, height: number, matrix : Matrix4 | null = null) : Matrix4 {
|
|
|
+ matrix = identity(matrix)
|
|
|
+ matrix[0] = 2. / width
|
|
|
+ matrix[5] = -2. / height
|
|
|
+ matrix[12] = -1
|
|
|
+ matrix[13] = 1
|
|
|
+ return matrix
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+ export function projectionNoflipY( width: number, height: number, matrix : Matrix4 | null = null) : Matrix4 {
|
|
|
+ matrix = identity(matrix)
|
|
|
+ matrix[0] = 2. / width
|
|
|
+ matrix[5] = 2. / height
|
|
|
+ matrix[12] = -1
|
|
|
+ matrix[13] = -1
|
|
|
+ return matrix
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+ export function scaleAt(scaleX : number, scaleY : number, focusX : number, focusY : number) : Matrix4 {
|
|
|
+ let matrix = identity()
|
|
|
+ matrix[0] = scaleX
|
|
|
+ matrix[5] = scaleY
|
|
|
+ matrix[12] = -scaleX * focusX + focusX
|
|
|
+ matrix[13] = -scaleY * focusY + focusY
|
|
|
+ return matrix
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ export function lerp(fromMat : Matrix4, toMat : Matrix4, outMat : Matrix4, t : number) {
|
|
|
+ for(var i=0; i<16; i++) {
|
|
|
+ outMat[i] = fromMat[i] + (toMat[i] - fromMat[i]) * t
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+}
|