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/**
* @module Math
* @submodule Trigonometry
* @for p5
* @requires core
* @requires constants
*/
import p5 from '../core/main';
import * as constants from '../core/constants';
/*
* all DEGREES/RADIANS conversion should be done in the p5 instance
* if possible, using the p5._toRadians(), p5._fromRadians() methods.
*/
p5.prototype._angleMode = constants.RADIANS;
/**
* Calculates the arc cosine of a number.
*
* `acos()` is the inverse of <a href="#/p5/cos">cos()</a>. It expects
* arguments in the range -1 to 1. By default, `acos()` returns values in the
* range 0 to π (about 3.14). If the
* <a href="#/p5/angleMode">angleMode()</a> is `DEGREES`, then values are
* returned in the range 0 to 180.
*
* @method acos
* @param {Number} value value whose arc cosine is to be returned.
* @return {Number} arc cosine of the given value.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate cos() and acos() values.
* let a = PI;
* let c = cos(a);
* let ac = acos(c);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(c, 3)}`, 35, 50);
* text(`${round(ac, 3)}`, 35, 75);
*
* describe('The numbers 3.142, -1, and 3.142 written on separate rows.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate cos() and acos() values.
* let a = PI + QUARTER_PI;
* let c = cos(a);
* let ac = acos(c);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(c, 3)}`, 35, 50);
* text(`${round(ac, 3)}`, 35, 75);
*
* describe('The numbers 3.927, -0.707, and 2.356 written on separate rows.');
* }
* </code>
* </div>
*/
p5.prototype.acos = function(ratio) {
return this._fromRadians(Math.acos(ratio));
};
/**
* Calculates the arc sine of a number.
*
* `asin()` is the inverse of <a href="#/p5/sin">sin()</a>. It expects input
* values in the range of -1 to 1. By default, `asin()` returns values in the
* range -π ÷ 2 (about -1.57) to π ÷ 2 (about 1.57). If
* the <a href="#/p5/angleMode">angleMode()</a> is `DEGREES` then values are
* returned in the range -90 to 90.
*
* @method asin
* @param {Number} value value whose arc sine is to be returned.
* @return {Number} arc sine of the given value.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate sin() and asin() values.
* let a = PI / 3;
* let s = sin(a);
* let as = asin(s);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(s, 3)}`, 35, 50);
* text(`${round(as, 3)}`, 35, 75);
*
* describe('The numbers 1.047, 0.866, and 1.047 written on separate rows.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate sin() and asin() values.
* let a = PI + PI / 3;
* let s = sin(a);
* let as = asin(s);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(s, 3)}`, 35, 50);
* text(`${round(as, 3)}`, 35, 75);
*
* describe('The numbers 4.189, -0.866, and -1.047 written on separate rows.');
* }
* </code>
* </div>
*/
p5.prototype.asin = function(ratio) {
return this._fromRadians(Math.asin(ratio));
};
/**
* Calculates the arc tangent of a number.
*
* `atan()` is the inverse of <a href="#/p5/tan">tan()</a>. It expects input
* values in the range of -Infinity to Infinity. By default, `atan()` returns
* values in the range -π ÷ 2 (about -1.57) to π ÷ 2
* (about 1.57). If the <a href="#/p5/angleMode">angleMode()</a> is `DEGREES`
* then values are returned in the range -90 to 90.
*
* @method atan
* @param {Number} value value whose arc tangent is to be returned.
* @return {Number} arc tangent of the given value.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate tan() and atan() values.
* let a = PI / 3;
* let t = tan(a);
* let at = atan(t);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(t, 3)}`, 35, 50);
* text(`${round(at, 3)}`, 35, 75);
*
* describe('The numbers 1.047, 1.732, and 1.047 written on separate rows.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate tan() and atan() values.
* let a = PI + PI / 3;
* let t = tan(a);
* let at = atan(t);
*
* // Display the values.
* text(`${round(a, 3)}`, 35, 25);
* text(`${round(t, 3)}`, 35, 50);
* text(`${round(at, 3)}`, 35, 75);
*
* describe('The numbers 4.189, 1.732, and 1.047 written on separate rows.');
* }
* </code>
* </div>
*/
p5.prototype.atan = function(ratio) {
return this._fromRadians(Math.atan(ratio));
};
/**
* Calculates the angle formed by a point, the origin, and the positive
* x-axis.
*
* `atan2()` is most often used for orienting geometry to the mouse's
* position, as in `atan2(mouseY, mouseX)`. The first parameter is the point's
* y-coordinate and the second parameter is its x-coordinate.
*
* By default, `atan2()` returns values in the range
* -π (about -3.14) to π (3.14). If the
* <a href="#/p5/angleMode">angleMode()</a> is `DEGREES`, then values are
* returned in the range -180 to 180.
*
* @method atan2
* @param {Number} y y-coordinate of the point.
* @param {Number} x x-coordinate of the point.
* @return {Number} arc tangent of the given point.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* describe('A rectangle at the top-left of the canvas rotates with mouse movements.');
* }
*
* function draw() {
* background(200);
*
* // Calculate the angle between the mouse
* // and the origin.
* let a = atan2(mouseY, mouseX);
*
* // Rotate.
* rotate(a);
*
* // Draw the shape.
* rect(0, 0, 60, 10);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* describe('A rectangle at the center of the canvas rotates with mouse movements.');
* }
*
* function draw() {
* background(200);
*
* // Translate the origin to the center.
* translate(50, 50);
*
* // Get the mouse's coordinates relative to the origin.
* let x = mouseX - 50;
* let y = mouseY - 50;
*
* // Calculate the angle between the mouse and the origin.
* let a = atan2(y, x);
*
* // Rotate.
* rotate(a);
*
* // Draw the shape.
* rect(-30, -5, 60, 10);
* }
* </code>
* </div>
*/
p5.prototype.atan2 = function(y, x) {
return this._fromRadians(Math.atan2(y, x));
};
/**
* Calculates the cosine of an angle.
*
* `cos()` is useful for many geometric tasks in creative coding. The values
* returned oscillate between -1 and 1 as the input angle increases. `cos()`
* calculates the cosine of an angle, using radians by default, or according to
* if <a href="#/p5/angleMode">angleMode()</a> setting (RADIANS or DEGREES).
*
* @method cos
* @param {Number} angle the angle, in radians by default, or according to
* if <a href="/reference/p5/angleMode/">angleMode()</a> setting (RADIANS or DEGREES).
* @return {Number} cosine of the angle.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* describe('A white ball on a string oscillates left and right.');
* }
*
* function draw() {
* background(200);
*
* // Calculate the coordinates.
* let x = 30 * cos(frameCount * 0.05) + 50;
* let y = 50;
*
* // Draw the oscillator.
* line(50, y, x, y);
* circle(x, y, 20);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* describe('A series of black dots form a wave pattern.');
* }
*
* function draw() {
* // Calculate the coordinates.
* let x = frameCount;
* let y = 30 * cos(x * 0.1) + 50;
*
* // Draw the point.
* point(x, y);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* describe('A series of black dots form an infinity symbol.');
* }
*
* function draw() {
* // Calculate the coordinates.
* let x = 30 * cos(frameCount * 0.1) + 50;
* let y = 10 * sin(frameCount * 0.2) + 50;
*
* // Draw the point.
* point(x, y);
* }
* </code>
* </div>
*/
p5.prototype.cos = function(angle) {
return Math.cos(this._toRadians(angle));
};
/**
* Calculates the sine of an angle.
*
* `sin()` is useful for many geometric tasks in creative coding. The values
* returned oscillate between -1 and 1 as the input angle increases. `sin()`
* calculates the sine of an angle, using radians by default, or according to
* if <a href="#/p5/angleMode">angleMode()</a> setting (RADIANS or DEGREES).
*
* @method sin
* @param {Number} angle the angle, in radians by default, or according to
* if <a href="/reference/p5/angleMode/">angleMode()</a> setting (RADIANS or DEGREES).
* @return {Number} sine of the angle.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* describe('A white ball on a string oscillates up and down.');
* }
*
* function draw() {
* background(200);
*
* // Calculate the coordinates.
* let x = 50;
* let y = 30 * sin(frameCount * 0.05) + 50;
*
* // Draw the oscillator.
* line(50, y, x, y);
* circle(x, y, 20);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* describe('A series of black dots form a wave pattern.');
* }
*
* function draw() {
* // Calculate the coordinates.
* let x = frameCount;
* let y = 30 * sin(x * 0.1) + 50;
*
* // Draw the point.
* point(x, y);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* describe('A series of black dots form an infinity symbol.');
* }
*
* function draw() {
* // Calculate the coordinates.
* let x = 30 * cos(frameCount * 0.1) + 50;
* let y = 10 * sin(frameCount * 0.2) + 50;
*
* // Draw the point.
* point(x, y);
* }
* </code>
* </div>
*/
p5.prototype.sin = function(angle) {
return Math.sin(this._toRadians(angle));
};
/**
* Calculates the tangent of an angle.
*
* `tan()` is useful for many geometric tasks in creative coding. The values
* returned range from -Infinity to Infinity and repeat periodically as the
* input angle increases. `tan()` calculates the tan of an angle, using radians
* by default, or according to
* if <a href="#/p5/angleMode">angleMode()</a> setting (RADIANS or DEGREES).
*
* @method tan
* @param {Number} angle the angle, in radians by default, or according to
* if <a href="/reference/p5/angleMode/">angleMode()</a> setting (RADIANS or DEGREES).
* @return {Number} tangent of the angle.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* describe('A series of identical curves drawn with black dots. Each curve starts from the top of the canvas, continues down at a slight angle, flattens out at the middle of the canvas, then continues to the bottom.');
* }
*
* function draw() {
* // Calculate the coordinates.
* let x = frameCount;
* let y = 5 * tan(x * 0.1) + 50;
*
* // Draw the point.
* point(x, y);
* }
* </code>
* </div>
*/
p5.prototype.tan = function(angle) {
return Math.tan(this._toRadians(angle));
};
/**
* Converts an angle measured in radians to its value in degrees.
*
* Degrees and radians are both units for measuring angles. There are 360˚ in
* one full rotation. A full rotation is 2 × π (about 6.28) radians.
*
* The same angle can be expressed in with either unit. For example, 90° is a
* quarter of a full rotation. The same angle is 2 × π ÷ 4
* (about 1.57) radians.
*
* @method degrees
* @param {Number} radians radians value to convert to degrees.
* @return {Number} converted angle.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate the angle conversion.
* let rad = QUARTER_PI;
* let deg = degrees(rad);
*
* // Display the conversion.
* text(`${round(rad, 2)} rad = ${deg}˚`, 10, 50);
*
* describe('The text "0.79 rad = 45˚".');
* }
* </code>
* </div>
*/
p5.prototype.degrees = angle => angle * constants.RAD_TO_DEG;
/**
* Converts an angle measured in degrees to its value in radians.
*
* Degrees and radians are both units for measuring angles. There are 360˚ in
* one full rotation. A full rotation is 2 × π (about 6.28) radians.
*
* The same angle can be expressed in with either unit. For example, 90° is a
* quarter of a full rotation. The same angle is 2 × π ÷ 4
* (about 1.57) radians.
*
* @method radians
* @param {Number} degrees degree value to convert to radians.
* @return {Number} converted angle.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Calculate the angle conversion.
* let deg = 45;
* let rad = radians(deg);
*
* // Display the angle conversion.
* text(`${deg}˚ = ${round(rad, 3)} rad`, 10, 50);
*
* describe('The text "45˚ = 0.785 rad".');
* }
* </code>
* </div>
*/
p5.prototype.radians = angle => angle * constants.DEG_TO_RAD;
/**
* Changes the unit system used to measure angles.
*
* Degrees and radians are both units for measuring angles. There are 360˚ in
* one full rotation. A full rotation is 2 × π (about 6.28) radians.
*
* Functions such as <a href="#/p5/rotate">rotate()</a> and
* <a href="#/p5/sin">sin()</a> expect angles measured radians by default.
* Calling `angleMode(DEGREES)` switches to degrees. Calling
* `angleMode(RADIANS)` switches back to radians.
*
* Calling `angleMode()` with no arguments returns current angle mode, which
* is either `RADIANS` or `DEGREES`.
*
* @method angleMode
* @param {Constant} mode either RADIANS or DEGREES.
*
* @example
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Rotate 1/8 turn.
* rotate(QUARTER_PI);
*
* // Draw a line.
* line(0, 0, 80, 0);
*
* describe('A diagonal line radiating from the top-left corner of a square.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Use degrees.
* angleMode(DEGREES);
*
* // Rotate 1/8 turn.
* rotate(45);
*
* // Draw a line.
* line(0, 0, 80, 0);
*
* describe('A diagonal line radiating from the top-left corner of a square.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(50);
*
* // Calculate the angle to rotate.
* let angle = TWO_PI / 7;
*
* // Move the origin to the center.
* translate(50, 50);
*
* // Style the flower.
* noStroke();
* fill(255, 50);
*
* // Draw the flower.
* for (let i = 0; i < 7; i += 1) {
* ellipse(0, 0, 80, 20);
* rotate(angle);
* }
*
* describe('A translucent white flower on a dark background.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(50);
*
* // Use degrees.
* angleMode(DEGREES);
*
* // Calculate the angle to rotate.
* let angle = 360 / 7;
*
* // Move the origin to the center.
* translate(50, 50);
*
* // Style the flower.
* noStroke();
* fill(255, 50);
*
* // Draw the flower.
* for (let i = 0; i < 7; i += 1) {
* ellipse(0, 0, 80, 20);
* rotate(angle);
* }
*
* describe('A translucent white flower on a dark background.');
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* describe('A white ball on a string oscillates left and right.');
* }
*
* function draw() {
* background(200);
*
* // Calculate the coordinates.
* let x = 30 * cos(frameCount * 0.05) + 50;
* let y = 50;
*
* // Draw the oscillator.
* line(50, y, x, y);
* circle(x, y, 20);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* // Use degrees.
* angleMode(DEGREES);
*
* describe('A white ball on a string oscillates left and right.');
* }
*
* function draw() {
* background(200);
*
* // Calculate the coordinates.
* let x = 30 * cos(frameCount * 2.86) + 50;
* let y = 50;
*
* // Draw the oscillator.
* line(50, y, x, y);
* circle(x, y, 20);
* }
* </code>
* </div>
*
* <div>
* <code>
* function setup() {
* createCanvas(100, 100);
*
* background(200);
*
* // Draw the upper line.
* rotate(PI / 6);
* line(0, 0, 80, 0);
*
* // Use degrees.
* angleMode(DEGREES);
*
* // Draw the lower line.
* rotate(30);
* line(0, 0, 80, 0);
*
* describe('Two diagonal lines radiating from the top-left corner of a square. The lines are oriented 30 degrees from the edges of the square and 30 degrees apart from each other.');
* }
* </code>
* </div>
*/
/**
* @method angleMode
* @return {Constant} mode either RADIANS or DEGREES
*/
p5.prototype.angleMode = function(mode) {
p5._validateParameters('angleMode', arguments);
if (typeof mode === 'undefined') {
return this._angleMode;
} else if (mode === constants.DEGREES || mode === constants.RADIANS) {
const prevMode = this._angleMode;
// No change
if(mode === prevMode) return;
// Otherwise adjust pRotation according to new mode
// This is necessary for acceleration events to work properly
if(mode === constants.RADIANS) {
// Change pRotation to radians
this._setProperty('pRotationX', this.pRotationX * constants.DEG_TO_RAD);
this._setProperty('pRotationY', this.pRotationY * constants.DEG_TO_RAD);
this._setProperty('pRotationZ', this.pRotationZ * constants.DEG_TO_RAD);
} else {
// Change pRotation to degrees
this._setProperty('pRotationX', this.pRotationX * constants.RAD_TO_DEG);
this._setProperty('pRotationY', this.pRotationY * constants.RAD_TO_DEG);
this._setProperty('pRotationZ', this.pRotationZ * constants.RAD_TO_DEG);
}
this._angleMode = mode;
}
};
/**
* converts angles from the current angleMode to RADIANS
*
* @method _toRadians
* @private
* @param {Number} angle
* @returns {Number}
*/
p5.prototype._toRadians = function(angle) {
if (this._angleMode === constants.DEGREES) {
return angle * constants.DEG_TO_RAD;
}
return angle;
};
/**
* converts angles from the current angleMode to DEGREES
*
* @method _toDegrees
* @private
* @param {Number} angle
* @returns {Number}
*/
p5.prototype._toDegrees = function(angle) {
if (this._angleMode === constants.RADIANS) {
return angle * constants.RAD_TO_DEG;
}
return angle;
};
/**
* converts angles from RADIANS into the current angleMode
*
* @method _fromRadians
* @private
* @param {Number} angle
* @returns {Number}
*/
p5.prototype._fromRadians = function(angle) {
if (this._angleMode === constants.DEGREES) {
return angle * constants.RAD_TO_DEG;
}
return angle;
};
/**
* converts angles from DEGREES into the current angleMode
*
* @method _fromDegrees
* @private
* @param {Number} angle
* @returns {Number}
*/
p5.prototype._fromDegrees = function(angle) {
if (this._angleMode === constants.RADIANS) {
return angle * constants.DEG_TO_RAD;
}
return angle;
};
export default p5;