Vec3

Calculates the cross product of two vectors.

Parameters

Example

The cross product of x and y unit vectors is the z unit vector.

var v1 = { x: 1, y: 0, z: 0 };
var v2 = { x: 0, y: 1, z: 0 };
var crossProduct = Vec3.cross(v1, v2);
print(JSON.stringify(crossProduct)); // {"x":0,"y":0,"z":1}

Calculates the distance between two points.

Parameters

Example

The distance between two points is aways positive.

var p1 = { x: 0, y: 0, z: 0 };
var p2 = { x: 0, y: 0, z: 10 };
var distance = Vec3.distance(p1, p2);
print(distance); // 10

p2 = { x: 0, y: 0, z: -10 };
distance = Vec3.distance(p1, p2);
print(distance); // 10

Calculates the dot product of two vectors.

Parameters

Example

The dot product of vectors at right angles is 0.

var v1 = { x: 1, y: 0, z: 0 };
var v2 = { x: 0, y: 1, z: 0 };
var dotProduct = Vec3.dot(v1, v2);
print(dotProduct); // 0

Tests whether two vectors are equal.

Note: The vectors must be exactly equal in order for true to be returned; it is often better to use withinEpsilon.

Parameters

Example

Vectors are only equal if exactly the same.

var v1 = { x: 10, y: 10, z: 10 };
var v2 = { x: 10, y: 10, z: 10 };

var equal = Vec3.equal(v1, v2);
print(equal);  // true

v2 = { x: 10, y: 10, z: 10.0005 };
equal = Vec3.equal(v1, v2);
print(equal);  // false

Calculates the coordinates of a point from polar coordinate transformation of the unit z-axis vector.

Parameters

Example

Polar coordinates to Cartesian.

var polar = { x: -19.471 * Math.PI / 180, y: 45 * Math.PI / 180, z: 7.5 };
var p = Vec3.fromPolar(polar);
print(JSON.stringify(p));  // {"x":5,"y":2.5,"z":5}

Calculates the unit vector corresponding to polar coordinates elevation and azimuth transformation of the unit z-axis vector.

Parameters

Example

Polar coordinates to Cartesian coordinates.

var elevation = -19.471 * Math.PI / 180;
var rotation = 45 * Math.PI / 180;
var p = Vec3.fromPolar(elevation, rotation);
print(JSON.stringify(p));  // {"x":0.667,"y":0.333,"z":0.667}
p = Vec3.multiply(7.5, p);
print(JSON.stringify(p));  // {"x":5,"y":2.5,"z":5}

Calculates the angle between two vectors.

Parameters

Example

Calculate the angle between two vectors.

var v1 = { x: 10, y: 0, z: 0 };
var v2 = { x: 0, y: 0, z: 10 };
var angle = Vec3.getAngle(v1, v2);
print(angle * 180 / Math.PI);  // 90
     

Calculates the length of a vector

Parameters

Calculates a linear interpolation between two vectors.

Parameters

Example

Linear interpolation between two vectors.

var v1 = { x: 10, y: 0, z: 0 };
var v2 = { x: 0, y: 10, z: 0 };
var interpolated = Vec3.mix(v1, v2, 0.75);  // 1/4 of v1 and 3/4 of v2.
print(JSON.stringify(interpolated));  // {"x":2.5,"y":7.5","z":0}

Multiplies a vector by a scale factor.

Parameters

Multiplies a vector by a scale factor.

Parameters

Rotates a vector.

Parameters

Example

Rotate the negative z-axis by 90 degrees about the x-axis.

var v = Vec3.UNIT_NEG_Z;
var q = Quat.fromPitchYawRollDegrees(90, 0, 0);
var result = Vec3.multiplyQbyV(q, v);
print(JSON.stringify(result));  // {"x":0,"y":1.000,"z":1.19e-7}

Multiplies two vectors.

Parameters

Example

Multiply two vectors.

var v1 = { x: 1, y: 2, z: 3 };
var v2 = { x: 1, y: 2, z: 3 };
var multiplied = Vec3.multiplyVbyV(v1, v2);
print(JSON.stringify(multiplied));  // {"x":1,"y":4,"z":9}

Normalizes a vector so that its length is 1.

Parameters

Example

Normalize a vector.

var v = { x: 10, y: 10, z: 0 };
var normalized = Vec3.normalize(v);
print(JSON.stringify(normalized));  // {"x":0.7071,"y":0.7071,"z":0}
print(Vec3.length(normalized));  // 1

Calculates the angle of rotation from one vector onto another, with the sign depending on a reference vector.

Parameters

Example

Compare Vec3.getAngle() and Vec3.orientedAngle().

var v1 = { x: 5, y: 0, z: 0 };
var v2 = { x: 5, y: 0, z: 5 };

var angle = Vec3.getAngle(v1, v2);
print(angle * 180 / Math.PI);  // 45

print(Vec3.orientedAngle(v1, v2, Vec3.UNIT_Y));  // -45
print(Vec3.orientedAngle(v1, v2, Vec3.UNIT_NEG_Y));  // 45
print(Vec3.orientedAngle(v1, v2, { x: 1, y: 2, z: -1 }));  // -45
print(Vec3.orientedAngle(v1, v2, { x: 1, y: -2, z: -1 }));  // 45

Prints the vector to the program log, as a text label followed by the vector value.

Parameters

Example

Two ways of printing a label and vector value.

var v = { x: 1, y: 2, z: 3 };
Vec3.print("Vector: ", v);  // dvec3(1.000000, 2.000000, 3.000000)
print("Vector: " + JSON.stringify(v));  // {"x":1,"y":2,"z":3}

Calculates the reflection of a vector in a plane.

Parameters

Example

Reflect a vector in the x-z plane.

var v = { x: 1, y: 2, z: 3 };
var normal = Vec3.UNIT_Y;
var reflected = Vec3.reflect(v, normal);
print(JSON.stringify(reflected));  // {"x":1,"y":-2,"z":3}

Calculates one vector subtracted from another.

Parameters

Calculates the sum of two vectors.

Parameters

Calculates polar coordinates (elevation, azimuth, radius) that transform the unit z-axis vector onto a point.

Parameters

Example

Polar coordinates for a point.

var v = { x: 5, y: 2.5, z: 5 };
var polar = Vec3.toPolar(v);
print("Elevation: " + polar.x * 180 / Math.PI);  // -19.471
print("Azimuth: " + polar.y * 180 / Math.PI);  // 45
print("Radius: " + polar.z);  // 7.5

Tests whether two vectors are equal within a tolerance.

Note: It is often better to use this function than equal.

Parameters

Example

Testing vectors for near equality.

var v1 = { x: 10, y: 10, z: 10 };
var v2 = { x: 10, y: 10, z: 10.0005 };

var equal = Vec3.equal(v1, v2);
print(equal);  // false

equal = Vec3.withinEpsilon(v1, v2, 0.001);
print(equal);  // true