@lightningjs/renderer
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Lightning 3 Renderer
693 lines • 21 kB
JavaScript
/*
* If not stated otherwise in this file or this component's LICENSE file the
* following copyright and licenses apply:
*
* Copyright 2023 Comcast Cable Communications Management, LLC.
*
* Licensed under the Apache License, Version 2.0 (the License);
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
import { ANGLE_ORDER, EPSILON, getMatrixArrayType, RANDOM, } from './common.js';
import * as mat3 from './mat3.js';
import * as vec3 from './vec3.js';
import * as vec4 from './vec4.js';
/**
* Quaternion in the format XYZW
* @module quat
*/
/**
* Creates a new identity quat
*
* @returns {quat} a new quaternion
*/
export function create() {
const out = getMatrixArrayType(4);
if (!(out instanceof Float32Array)) {
out[0] = 0;
out[1] = 0;
out[2] = 0;
}
out[3] = 1;
return out;
}
/**
* Set a quat to the identity quaternion
*
* @param {quat} out the receiving quaternion
* @returns {quat} out
*/
export function identity(out) {
out[0] = 0;
out[1] = 0;
out[2] = 0;
out[3] = 1;
return out;
}
/**
* Sets a quat from the given angle and rotation axis,
* then returns it.
*
* @param {quat} out the receiving quaternion
* @param {Vec3} axis the axis around which to rotate
* @param {Number} rad the angle in radians
* @returns {quat} out
**/
export function setAxisAngle(out, axis, rad) {
rad = rad * 0.5;
const 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.
* @param {Vec3} out_axis Vector receiving the axis of rotation
* @param {Quat} q Quaternion to be decomposed
* @return {Number} Angle, in radians, of the rotation
*/
export function getAxisAngle(out_axis, q) {
const rad = Math.acos(q[3]) * 2.0;
const s = Math.sin(rad / 2.0);
if (s > EPSILON) {
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;
}
/**
* Gets the angular distance between two unit quaternions
*
* @param {Quat} a Origin unit quaternion
* @param {Quat} b Destination unit quaternion
* @return {Number} Angle, in radians, between the two quaternions
*/
export function getAngle(a, b) {
const dotproduct = dot(a, b);
return Math.acos(2 * dotproduct * dotproduct - 1);
}
/**
* Multiplies two quat's
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @returns {quat} out
*/
export function multiply(out, a, b) {
const ax = a[0], ay = a[1], az = a[2], aw = a[3];
const 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;
}
/**
* Rotates a quaternion by the given angle about the X axis
*
* @param {quat} out quat receiving operation result
* @param {Quat} a quat to rotate
* @param {number} rad angle (in radians) to rotate
* @returns {quat} out
*/
export function rotateX(out, a, rad) {
rad *= 0.5;
const ax = a[0], ay = a[1], az = a[2], aw = a[3];
const 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;
}
/**
* Rotates a quaternion by the given angle about the Y axis
*
* @param {quat} out quat receiving operation result
* @param {Quat} a quat to rotate
* @param {number} rad angle (in radians) to rotate
* @returns {quat} out
*/
export function rotateY(out, a, rad) {
rad *= 0.5;
const ax = a[0], ay = a[1], az = a[2], aw = a[3];
const 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;
}
/**
* Rotates a quaternion by the given angle about the Z axis
*
* @param {quat} out quat receiving operation result
* @param {Quat} a quat to rotate
* @param {number} rad angle (in radians) to rotate
* @returns {quat} out
*/
export function rotateZ(out, a, rad) {
rad *= 0.5;
const ax = a[0], ay = a[1], az = a[2], aw = a[3];
const 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.
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate W component of
* @returns {quat} out
*/
export function calculateW(out, a) {
const 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;
}
/**
* Calculate the exponential of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate the exponential of
* @returns {quat} out
*/
export function exp(out, a) {
const x = a[0], y = a[1], z = a[2], w = a[3];
const r = Math.sqrt(x * x + y * y + z * z);
const et = Math.exp(w);
const s = r > 0 ? (et * Math.sin(r)) / r : 0;
out[0] = x * s;
out[1] = y * s;
out[2] = z * s;
out[3] = et * Math.cos(r);
return out;
}
/**
* Calculate the natural logarithm of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate the exponential of
* @returns {quat} out
*/
export function ln(out, a) {
const x = a[0], y = a[1], z = a[2], w = a[3];
const r = Math.sqrt(x * x + y * y + z * z);
const t = r > 0 ? Math.atan2(r, w) / r : 0;
out[0] = x * t;
out[1] = y * t;
out[2] = z * t;
out[3] = 0.5 * Math.log(x * x + y * y + z * z + w * w);
return out;
}
/**
* Calculate the scalar power of a unit quaternion.
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate the exponential of
* @param {Number} b amount to scale the quaternion by
* @returns {quat} out
*/
export function pow(out, a, b) {
ln(out, a);
scale(out, out, b);
exp(out, out);
return out;
}
/**
* Performs a spherical linear interpolation between two quat
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
*/
export function slerp(out, a, b, t) {
// benchmarks:
// http://jsperf.com/quaternion-slerp-implementations
const 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 > EPSILON) {
// 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;
}
/**
* Generates a random unit quaternion
*
* @param {quat} out the receiving quaternion
* @returns {quat} out
*/
export function random(out) {
// Implementation of http://planning.cs.uiuc.edu/node198.html
// TODO: Calling random 3 times is probably not the fastest solution
const u1 = RANDOM();
const u2 = RANDOM();
const u3 = RANDOM();
const sqrt1MinusU1 = Math.sqrt(1 - u1);
const sqrtU1 = Math.sqrt(u1);
out[0] = sqrt1MinusU1 * Math.sin(2.0 * Math.PI * u2);
out[1] = sqrt1MinusU1 * Math.cos(2.0 * Math.PI * u2);
out[2] = sqrtU1 * Math.sin(2.0 * Math.PI * u3);
out[3] = sqrtU1 * Math.cos(2.0 * Math.PI * u3);
return out;
}
/**
* Calculates the inverse of a quat
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate inverse of
* @returns {quat} out
*/
export function invert(out, a) {
const a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
const 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.
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quat to calculate conjugate of
* @returns {quat} out
*/
export function conjugate(out, a) {
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.
*
* @param {quat} out the receiving quaternion
* @param {Mat3} m rotation matrix
* @returns {quat} out
* @function
*/
export function fromMat3(out, m) {
// 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 {
let i = 0;
if (m[4] > m[0])
i = 1;
if (m[8] > m[(i * 3 + i)])
i = 2;
const j = ((i + 1) % 3);
const 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;
}
/**
* Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.
*
* @param {quat} out the receiving quaternion
* @param {x} x Angle to rotate around X axis in degrees.
* @param {y} y Angle to rotate around Y axis in degrees.
* @param {z} z Angle to rotate around Z axis in degrees.
* @param {'zyx'|'xyz'|'yxz'|'yzx'|'zxy'|'zyx'} order Intrinsic order for conversion, default is zyx.
* @returns {quat} out
* @function
*/
export function fromEuler(out, x, y, z, order) {
order = order ?? ANGLE_ORDER;
const halfToRad = Math.PI / 360;
x *= halfToRad;
z *= halfToRad;
y *= halfToRad;
const sx = Math.sin(x);
const cx = Math.cos(x);
const sy = Math.sin(y);
const cy = Math.cos(y);
const sz = Math.sin(z);
const cz = Math.cos(z);
switch (order) {
case 'xyz':
out[0] = sx * cy * cz + cx * sy * sz;
out[1] = cx * sy * cz - sx * cy * sz;
out[2] = cx * cy * sz + sx * sy * cz;
out[3] = cx * cy * cz - sx * sy * sz;
break;
case 'xzy':
out[0] = sx * cy * cz - cx * sy * sz;
out[1] = cx * sy * cz - sx * cy * sz;
out[2] = cx * cy * sz + sx * sy * cz;
out[3] = cx * cy * cz + sx * sy * sz;
break;
case 'yxz':
out[0] = sx * cy * cz + cx * sy * sz;
out[1] = cx * sy * cz - sx * cy * sz;
out[2] = cx * cy * sz - sx * sy * cz;
out[3] = cx * cy * cz + sx * sy * sz;
break;
case 'yzx':
out[0] = sx * cy * cz + cx * sy * sz;
out[1] = cx * sy * cz + sx * cy * sz;
out[2] = cx * cy * sz - sx * sy * cz;
out[3] = cx * cy * cz - sx * sy * sz;
break;
case 'zxy':
out[0] = sx * cy * cz - cx * sy * sz;
out[1] = cx * sy * cz + sx * cy * sz;
out[2] = cx * cy * sz + sx * sy * cz;
out[3] = cx * cy * cz - sx * sy * sz;
break;
case 'zyx':
out[0] = sx * cy * cz - cx * sy * sz;
out[1] = cx * sy * cz + sx * cy * sz;
out[2] = cx * cy * sz - sx * sy * cz;
out[3] = cx * cy * cz + sx * sy * sz;
break;
default:
throw new Error('Unknown angle order ' + order);
}
return out;
}
/**
* Returns a string representation of a quaternion
*
* @param {Quat} a vector to represent as a string
* @returns {String} string representation of the vector
*/
export function str(a) {
return `quat(${a[0]}, ${a[1]}, ${a[2]}, ${a[3]})`;
}
/**
* Creates a new quat initialized with values from an existing quaternion
*
* @param {Quat} a quaternion to clone
* @returns {quat} a new quaternion
* @function
*/
export const clone = vec4.clone;
/**
* Creates a new quat initialized with the given values
*
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @param {Number} w W component
* @returns {quat} a new quaternion
* @function
*/
export const fromValues = vec4.fromValues;
/**
* Copy the values from one quat to another
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the source quaternion
* @returns {quat} out
* @function
*/
export const copy = vec4.copy;
/**
* Set the components of a quat to the given values
*
* @param {quat} out the receiving quaternion
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @param {Number} w W component
* @returns {quat} out
* @function
*/
export const set = vec4.set;
/**
* Adds two quat's
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @returns {quat} out
* @function
*/
export const add = vec4.add;
/**
* Alias for {@link quat.multiply}
* @function
*/
export const mul = multiply;
/**
* Scales a quat by a scalar number
*
* @param {quat} out the receiving vector
* @param {Quat} a the vector to scale
* @param {Number} b amount to scale the vector by
* @returns {quat} out
* @function
*/
export const scale = vec4.scale;
/**
* Calculates the dot product of two quat's
*
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @returns {Number} dot product of a and b
* @function
*/
export const dot = vec4.dot;
/**
* Performs a linear interpolation between two quat's
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
* @function
*/
export const lerp = vec4.lerp;
/**
* Calculates the length of a quat
*
* @param {Quat} a vector to calculate length of
* @returns {Number} length of a
*/
export const length = vec4.length;
/**
* Alias for {@link length}
* @function
*/
export const len = length;
/**
* Calculates the squared length of a quat
*
* @param {Quat} a vector to calculate squared length of
* @returns {Number} squared length of a
* @function
*/
export const squaredLength = vec4.squaredLength;
/**
* Alias for {@link squaredLength}
* @function
*/
export const sqrLen = squaredLength;
/**
* Normalize a quat
*
* @param {quat} out the receiving quaternion
* @param {Quat} a quaternion to normalize
* @returns {quat} out
* @function
*/
export const normalize = vec4.normalize;
/**
* Returns whether or not the quaternions have exactly the same elements in the same position (when compared with ===)
*
* @param {Quat} a The first quaternion.
* @param {Quat} b The second quaternion.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
export const exactEquals = vec4.exactEquals;
/**
* Returns whether or not the quaternions point approximately to the same direction.
*
* Both quaternions are assumed to be unit length.
*
* @param {Quat} a The first unit quaternion.
* @param {Quat} b The second unit quaternion.
* @returns {Boolean} True if the quaternions are equal, false otherwise.
*/
export function equals(a, b) {
return Math.abs(vec4.dot(a, b)) >= 1 - EPSILON;
}
/**
* Sets a quaternion to represent the shortest rotation from one
* vector to another.
*
* Both vectors are assumed to be unit length.
*
* @param {quat} out the receiving quaternion.
* @param {Vec3} a the initial vector
* @param {Vec3} b the destination vector
* @returns {quat} out
*/
export const rotationTo = (function () {
const tmpVec3 = vec3.create();
const xUnitVec3 = vec3.fromValues(1, 0, 0);
const yUnitVec3 = vec3.fromValues(0, 1, 0);
return function (out, a, b) {
const dot = vec3.dot(a, b);
if (dot < -0.999999) {
vec3.cross(tmpVec3, xUnitVec3, a);
if (vec3.len(tmpVec3) < 0.000001)
vec3.cross(tmpVec3, yUnitVec3, a);
vec3.normalize(tmpVec3, tmpVec3);
setAxisAngle(out, tmpVec3, 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(tmpVec3, a, b);
out[0] = tmpVec3[0];
out[1] = tmpVec3[1];
out[2] = tmpVec3[2];
out[3] = 1 + dot;
return normalize(out, out);
}
};
})();
/**
* Performs a spherical linear interpolation with two control points
*
* @param {quat} out the receiving quaternion
* @param {Quat} a the first operand
* @param {Quat} b the second operand
* @param {Quat} c the third operand
* @param {Quat} d the fourth operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {quat} out
*/
export const sqlerp = (function () {
const temp1 = create();
const temp2 = create();
return function (out, a, b, c, d, t) {
slerp(temp1, a, d, t);
slerp(temp2, b, c, t);
slerp(out, temp1, temp2, 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.
*
* @param {Vec3} view the vector representing the viewing direction
* @param {Vec3} right the vector representing the local "right" direction
* @param {Vec3} up the vector representing the local "up" direction
* @returns {quat} out
*/
export const setAxes = (function () {
const matr = mat3.create();
return function (out, view, right, up) {
matr[0] = right[0];
matr[3] = right[1];
matr[6] = right[2];
matr[1] = up[0];
matr[4] = up[1];
matr[7] = up[2];
matr[2] = -view[0];
matr[5] = -view[1];
matr[8] = -view[2];
return normalize(out, fromMat3(out, matr));
};
})();
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