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260 lines (239 loc) · 8.83 KB
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/**
* @name pc.math
* @namespace
* @description Math API
*/
pc.math = {
/**
* @name pc.math.DEG_TO_RAD
* @description Conversion factor between degrees and radians
* @type Number
* @example
* // Convert 180 degrees to pi radians
* var rad = 180 * pc.math.DEG_TO_RAD;
*/
DEG_TO_RAD: Math.PI / 180,
/**
* @name pc.math.RAD_TO_DEG
* @description Conversion factor between degrees and radians
* @type Number
* @example
* // Convert pi radians to 180 degrees
* var deg = Math.PI * pc.math.RAD_TO_DEG;
*/
RAD_TO_DEG: 180 / Math.PI,
/**
* @function
* @name pc.math.clamp
* @description Clamp a number between min and max inclusive.
* @param {Number} value Number to clamp
* @param {Number} min Min value
* @param {Number} max Max value
* @returns {Number} The clamped value
*/
clamp: function (value, min, max) {
if (value >= max) return max;
if (value <= min) return min;
return value;
},
/**
* @function
* @name pc.math.intToBytes24
* @description Convert an 24 bit integer into an array of 3 bytes.
* @param {Number} i Number holding an integer value
* @returns {Number[]} An array of 3 bytes.
* @example
* // Set bytes to [0x11, 0x22, 0x33]
* var bytes = pc.math.intToBytes24(0x112233);
*/
intToBytes24: function (i) {
var r, g, b;
r = (i >> 16) & 0xff;
g = (i >> 8) & 0xff;
b = (i) & 0xff;
return [r, g, b];
},
/**
* @function
* @name pc.math.intToBytes32
* @description Convert an 32 bit integer into an array of 4 bytes.
* @returns {Number[]} An array of 4 bytes
* @param {Number} i Number holding an integer value
* @example
* // Set bytes to [0x11, 0x22, 0x33, 0x44]
* var bytes = pc.math.intToBytes32(0x11223344);
*/
intToBytes32: function (i) {
var r, g, b, a;
r = (i >> 24) & 0xff;
g = (i >> 16) & 0xff;
b = (i >> 8) & 0xff;
a = (i) & 0xff;
return [r, g, b, a];
},
/**
* @function
* @name pc.math.bytesToInt24
* @description Convert 3 8 bit Numbers into a single unsigned 24 bit Number.
* @example
* // Set result1 to 0x112233 from an array of 3 values
* var result1 = pc.math.bytesToInt24([0x11, 0x22, 0x33]);
*
* // Set result2 to 0x112233 from 3 discrete values
* var result2 = pc.math.bytesToInt24(0x11, 0x22, 0x33);
* @param {Number} r A single byte (0-255)
* @param {Number} g A single byte (0-255)
* @param {Number} b A single byte (0-255)
* @returns {Number} A single unsigned 24 bit Number.
*/
bytesToInt24: function (r, g, b) {
if (r.length) {
b = r[2];
g = r[1];
r = r[0];
}
return ((r << 16) | (g << 8) | b);
},
/**
* @function
* @name pc.math.bytesToInt32
* @description Convert 4 1-byte Numbers into a single unsigned 32bit Number.
* @returns {Number} A single unsigned 32bit Number.
* @example
* // Set result1 to 0x11223344 from an array of 4 values
* var result1 = pc.math.bytesToInt32([0x11, 0x22, 0x33, 0x44]);
*
* // Set result2 to 0x11223344 from 4 discrete values
* var result2 = pc.math.bytesToInt32(0x11, 0x22, 0x33, 0x44);
* @param {Number} r A single byte (0-255)
* @param {Number} g A single byte (0-255)
* @param {Number} b A single byte (0-255)
* @param {Number} a A single byte (0-255)
*/
bytesToInt32: function (r, g, b, a) {
if (r.length) {
a = r[3];
b = r[2];
g = r[1];
r = r[0];
}
// Why ((r << 24)>>>32)?
// << operator uses signed 32 bit numbers, so 128<<24 is negative.
// >>> used unsigned so >>>32 converts back to an unsigned.
// See http://stackoverflow.com/questions/1908492/unsigned-integer-in-javascript
return ((r << 24) | (g << 16) | (b << 8) | a) >>> 32;
},
/**
* @function
* @name pc.math.lerp
* @returns {Number} The linear interpolation of two numbers.
* @description Calculates the linear interpolation of two numbers.
* @param {Number} a Number to linearly interpolate from.
* @param {Number} b Number to linearly interpolate to.
* @param {Number} alpha The value controlling the result of interpolation. When alpha is 0,
* a is returned. When alpha is 1, b is returned. Between 0 and 1, a linear interpolation between
* a and b is returned. alpha is clamped between 0 and 1.
*/
lerp: function (a, b, alpha) {
return a + (b - a) * pc.math.clamp(alpha, 0, 1);
},
/**
* @function
* @name pc.math.lerpAngle
* @description Calculates the linear interpolation of two angles ensuring that interpolation
* is correctly performed across the 360 to 0 degree boundary. Angles are supplied in degrees.
* @returns {Number} The linear interpolation of two angles
* @param {Number} a Angle (in degrees) to linearly interpolate from.
* @param {Number} b Angle (in degrees) to linearly interpolate to.
* @param {Number} alpha The value controlling the result of interpolation. When alpha is 0,
* a is returned. When alpha is 1, b is returned. Between 0 and 1, a linear interpolation between
* a and b is returned. alpha is clamped between 0 and 1.
*/
lerpAngle: function (a, b, alpha) {
if (b - a > 180 ) {
b -= 360;
}
if (b - a < -180 ) {
b += 360;
}
return pc.math.lerp(a, b, pc.math.clamp(alpha, 0, 1));
},
/**
* @function
* @name pc.math.powerOfTwo
* @description Returns true if argument is a power-of-two and false otherwise.
* @param {Number} x Number to check for power-of-two property.
* @returns {Boolean} true if power-of-two and false otherwise.
*/
powerOfTwo: function (x) {
return ((x !== 0) && !(x & (x - 1)));
},
/**
* @function
* @name pc.math.nextPowerOfTwo
* @description Returns the next power of 2 for the specified value.
* @param {Number} val The value for which to calculate the next power of 2.
* @returns {Number} The next power of 2.
*/
nextPowerOfTwo: function (val) {
val--;
val |= (val >> 1);
val |= (val >> 2);
val |= (val >> 4);
val |= (val >> 8);
val |= (val >> 16);
val++;
return val;
},
/**
* @function
* @name pc.math.random
* @description Return a pseudo-random number between min and max.
* The number generated is in the range [min, max), that is inclusive of the minimum but exclusive of the maximum.
* @param {Number} min Lower bound for range.
* @param {Number} max Upper bound for range.
* @returns {Number} Pseudo-random number between the supplied range.
*/
random: function (min, max) {
var diff = max - min;
return Math.random() * diff + min;
},
/**
* @function
* @name pc.math.smoothstep
* @description The function interpolates smoothly between two input values based on
* a third one that should be between the first two. The returned value is clamped
* between 0 and 1.
* <br/>The slope (i.e. derivative) of the smoothstep function starts at 0 and ends at 0.
* This makes it easy to create a sequence of transitions using smoothstep to interpolate
* each segment rather than using a more sophisticated or expensive interpolation technique.
* <br/>See http://en.wikipedia.org/wiki/Smoothstep for more details.
* @param {Number} min The lower bound of the interpolation range.
* @param {Number} max The upper bound of the interpolation range.
* @param {Number} x The value to interpolate.
* @returns {Number} The smoothly interpolated value clamped between zero and one.
*/
smoothstep: function (min, max, x) {
if (x <= min) return 0;
if (x >= max) return 1;
x = (x - min) / (max - min);
return x * x * (3 - 2 * x);
},
/**
* @function
* @name pc.math.smootherstep
* @description An improved version of the pc.math.smoothstep function which has zero
* 1st and 2nd order derivatives at t=0 and t=1.
* <br/>See http://en.wikipedia.org/wiki/Smoothstep for more details.
* @param {Number} min The lower bound of the interpolation range.
* @param {Number} max The upper bound of the interpolation range.
* @param {Number} x The value to interpolate.
* @returns {Number} The smoothly interpolated value clamped between zero and one.
*/
smootherstep: function (min, max, x) {
if (x <= min) return 0;
if (x >= max) return 1;
x = (x - min) / (max - min);
return x * x * x * (x * (x * 6 - 15) + 10);
}
};