Ueda's AttractorJacobi Elliptic Functions in the Complex PlaneSDF Points with reglClifford and de Jong AttractorsDrawing Instanced Lines with reglInstanced Line RenderingLawson's Klein BottleInteractive Multi-scale Turing PatternsSelecting the Right Opacity for 2D Point CloudsAdaptive Contouring in Fragment ShadersBaker's MapFake Transparency for 3D SurfacesGPU BoidsDouble Compound Pendulums3D Reaction-DiffusionMathematical Easter Egg ColoringToiletpaperfullerenes and Charmin NanotubesQuasicrystalsObservable + regl2D (Non-physical) N-body Gravity with Poisson's EquationPeriodic Planar Three-Body OrbitsQuick (miterless) Lines in WebGLSpin WebGLicosphereregl-cameraFinding Roots in the Complex Planeglsl-complexglsl-complex-auto-differentiationDomain Coloring with Adaptive Contouringgl-mat3gl-vec4gl-quatgl-mat2gl-vec3gl-vec2Instanced WebGL Circlesregl-toolsDomain Coloring for Complex FunctionsContour Plots with regl Observable PlotDrawing indexed mesh data as screen-space normals without duplicating dataGPUs, FFTs, and the 1-D Schrödinger Equation
gl-mat4
a = mat4.create()
b = mat4create()
mat4 = ({
EPSILON,
equals: mat4equals,
create: mat4create,
clone: mat4clone,
copy: mat4copy,
identity: mat4identity,
transpose: mat4transpose,
invert: mat4invert,
adjoint: mat4adjoint,
determinant: mat4determinant,
multiply: mat4multiply,
translate: mat4translate,
scale: mat4scale,
rotate: mat4rotate,
rotateX: mat4rotateX,
rotateY: mat4rotateY,
rotateZ: mat4rotateZ,
fromMat3: mat4fromMat3,
fromRotation: mat4fromRotation,
fromRotationTranslation: mat4fromRotationTranslation,
fromScaling: mat4fromScaling,
fromTranslation: mat4fromTranslation,
fromXRotation: mat4fromXRotation,
fromYRotation: mat4fromYRotation,
fromZRotation: mat4fromZRotation,
fromQuat: mat4fromQuat,
frustum: mat4frustum,
perspective: mat4perspective,
perspectiveFromFieldOfView: mat4perspectiveFromFieldOfView,
ortho: mat4ortho,
lookAt: mat4lookAt,
str: mat4str
})
EPSILON = 0.000001
/**
* Calculates the adjugate of a mat4
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the source matrix
* @returns {mat4} out
*/
function mat4adjoint(out, a) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
out[0] = (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
out[2] = (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
out[5] = (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
out[7] = (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
out[8] = (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
out[10] = (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
out[13] = (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
out[15] = (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));
return out;
};
/**
* Creates a new mat4 initialized with values from an existing matrix
*
* @param {mat4} a matrix to clone
* @returns {mat4} a new 4x4 matrix
*/
function mat4clone(a) {
var out = new Float32Array(16);
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
};
/**
* Copy the values from one mat4 to another
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the source matrix
* @returns {mat4} out
*/
function mat4copy(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
};
/**
* Returns whether or not the vectors have approximately the same elements in the same position.
*
* @param {vec3} a The first vector.
* @param {vec3} b The second vector.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
// prettier-ignore
function mat4equals(a, b) {
const a0 = a[0], b0 = b[0];
const a1 = a[1], b1 = b[1];
const a2 = a[2], b2 = b[2];
const a3 = a[3], b3 = b[3];
const a4 = a[4], b4 = b[4];
const a5 = a[5], b5 = b[5];
const a6 = a[6], b6 = b[6];
const a7 = a[7], b7 = b[7];
const a8 = a[8], b8 = b[8];
const a9 = a[9], b9 = b[9];
const a10 = a[10], b10 = b[10];
const a11 = a[11], b11 = b[11];
const a12 = a[12], b12 = b[12];
const a13 = a[13], b13 = b[13];
const a14 = a[14], b14 = b[14];
const a15 = a[15], b15 = b[15];
return (Math.abs(a0 - b0) <= EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
Math.abs(a1 - b1) <= EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
Math.abs(a2 - b2) <= EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
Math.abs(a3 - b3) <= EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) &&
Math.abs(a4 - b4) <= EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) &&
Math.abs(a5 - b5) <= EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) &&
Math.abs(a6 - b6) <= EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) &&
Math.abs(a7 - b7) <= EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) &&
Math.abs(a8 - b8) <= EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) &&
Math.abs(a9 - b9) <= EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) &&
Math.abs(a10 - b10) <= EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) &&
Math.abs(a11 - b11) <= EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) &&
Math.abs(a12 - b12) <= EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) &&
Math.abs(a13 - b13) <= EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) &&
Math.abs(a14 - b14) <= EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) &&
Math.abs(a15 - b15) <= EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15))
);
}
/**
* Creates a new identity mat4
*
* @returns {mat4} a new 4x4 matrix
*/
function mat4create() {
var out = new Float32Array(16);
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
};
/**
* Calculates the determinant of a mat4
*
* @param {mat4} a the source matrix
* @returns {Number} determinant of a
*/
function mat4determinant(a) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
b00 = a00 * a11 - a01 * a10,
b01 = a00 * a12 - a02 * a10,
b02 = a00 * a13 - a03 * a10,
b03 = a01 * a12 - a02 * a11,
b04 = a01 * a13 - a03 * a11,
b05 = a02 * a13 - a03 * a12,
b06 = a20 * a31 - a21 * a30,
b07 = a20 * a32 - a22 * a30,
b08 = a20 * a33 - a23 * a30,
b09 = a21 * a32 - a22 * a31,
b10 = a21 * a33 - a23 * a31,
b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
};
/**
* Creates a matrix from a quaternion rotation.
*
* @param {mat4} out mat4 receiving operation result
* @param {quat4} q Rotation quaternion
* @returns {mat4} out
*/
function mat4fromQuat(out, q) {
var x = q[0], y = q[1], z = q[2], w = q[3],
x2 = x + x,
y2 = y + y,
z2 = z + z,
xx = x * x2,
yx = y * x2,
yy = y * y2,
zx = z * x2,
zy = z * y2,
zz = z * z2,
wx = w * x2,
wy = w * y2,
wz = w * z2;
out[0] = 1 - yy - zz;
out[1] = yx + wz;
out[2] = zx - wy;
out[3] = 0;
out[4] = yx - wz;
out[5] = 1 - xx - zz;
out[6] = zy + wx;
out[7] = 0;
out[8] = zx + wy;
out[9] = zy - wx;
out[10] = 1 - xx - yy;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
};
/**
* Creates a matrix from a given angle around a given axis
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.rotate(dest, dest, rad, axis)
*
* @param {mat4} out mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @param {vec3} axis the axis to rotate around
* @returns {mat4} out
*/
function mat4fromRotation(out, rad, axis) {
var s, c, t
var x = axis[0]
var y = axis[1]
var z = axis[2]
var len = Math.sqrt(x * x + y * y + z * z)
if (Math.abs(len) < 0.000001) {
return null
}
len = 1 / len
x *= len
y *= len
z *= len
s = Math.sin(rad)
c = Math.cos(rad)
t = 1 - c
// Perform rotation-specific matrix multiplication
out[0] = x * x * t + c
out[1] = y * x * t + z * s
out[2] = z * x * t - y * s
out[3] = 0
out[4] = x * y * t - z * s
out[5] = y * y * t + c
out[6] = z * y * t + x * s
out[7] = 0
out[8] = x * z * t + y * s
out[9] = y * z * t - x * s
out[10] = z * z * t + c
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}
/**
* Creates a matrix from a quaternion rotation and vector translation
* This is equivalent to (but much faster than):
*
* mat4.identity(dest);
* mat4.translate(dest, vec);
* var quatMat = mat4.create();
* quat4.toMat4(quat, quatMat);
* mat4.multiply(dest, quatMat);
*
* @param {mat4} out mat4 receiving operation result
* @param {quat4} q Rotation quaternion
* @param {vec3} v Translation vector
* @returns {mat4} out
*/
function mat4fromRotationTranslation(out, q, v) {
// Quaternion math
var x = q[0], y = q[1], z = q[2], w = q[3],
x2 = x + x,
y2 = y + y,
z2 = z + z,
xx = x * x2,
xy = x * y2,
xz = x * z2,
yy = y * y2,
yz = y * z2,
zz = z * z2,
wx = w * x2,
wy = w * y2,
wz = w * z2;
out[0] = 1 - (yy + zz);
out[1] = xy + wz;
out[2] = xz - wy;
out[3] = 0;
out[4] = xy - wz;
out[5] = 1 - (xx + zz);
out[6] = yz + wx;
out[7] = 0;
out[8] = xz + wy;
out[9] = yz - wx;
out[10] = 1 - (xx + yy);
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out;
};
/**
* Creates a matrix from a 2d homogeneous transformation matrix. The
* z component receives the identity matrix components.
*
* @param {mat4} out mat4 receiving operation result
* @param {mat3} a input transformation matrix
* @returns {mat4} out
*/
function mat4fromMat3 (out, a) {
out[0] = a[0]
out[1] = a[1]
out[2] = 0
out[3] = a[2]
out[4] = a[3]
out[5] = a[4]
out[6] = 0
out[7] = a[5]
out[8] = 0
out[9] = 0
out[10] = 1
out[11] = 0
out[12] = a[6]
out[13] = a[7]
out[14] = 0
out[15] = a[8]
}
/**
* Creates a matrix from a vector scaling
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.scale(dest, dest, vec)
*
* @param {mat4} out mat4 receiving operation result
* @param {vec3} v Scaling vector
* @returns {mat4} out
*/
function mat4fromScaling(out, v) {
out[0] = v[0]
out[1] = 0
out[2] = 0
out[3] = 0
out[4] = 0
out[5] = v[1]
out[6] = 0
out[7] = 0
out[8] = 0
out[9] = 0
out[10] = v[2]
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}
/**
* Creates a matrix from a vector translation
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.translate(dest, dest, vec)
*
* @param {mat4} out mat4 receiving operation result
* @param {vec3} v Translation vector
* @returns {mat4} out
*/
function mat4fromTranslation(out, v) {
out[0] = 1
out[1] = 0
out[2] = 0
out[3] = 0
out[4] = 0
out[5] = 1
out[6] = 0
out[7] = 0
out[8] = 0
out[9] = 0
out[10] = 1
out[11] = 0
out[12] = v[0]
out[13] = v[1]
out[14] = v[2]
out[15] = 1
return out
}
/**
* Creates a matrix from the given angle around the X axis
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.rotateX(dest, dest, rad)
*
* @param {mat4} out mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4fromXRotation(out, rad) {
var s = Math.sin(rad),
c = Math.cos(rad)
// Perform axis-specific matrix multiplication
out[0] = 1
out[1] = 0
out[2] = 0
out[3] = 0
out[4] = 0
out[5] = c
out[6] = s
out[7] = 0
out[8] = 0
out[9] = -s
out[10] = c
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}
/**
* Creates a matrix from the given angle around the Y axis
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.rotateY(dest, dest, rad)
*
* @param {mat4} out mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4fromYRotation(out, rad) {
var s = Math.sin(rad),
c = Math.cos(rad)
// Perform axis-specific matrix multiplication
out[0] = c
out[1] = 0
out[2] = -s
out[3] = 0
out[4] = 0
out[5] = 1
out[6] = 0
out[7] = 0
out[8] = s
out[9] = 0
out[10] = c
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}
/**
* Creates a matrix from the given angle around the Z axis
* This is equivalent to (but much faster than):
*
* mat4.identity(dest)
* mat4.rotateZ(dest, dest, rad)
*
* @param {mat4} out mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4fromZRotation(out, rad) {
var s = Math.sin(rad),
c = Math.cos(rad)
// Perform axis-specific matrix multiplication
out[0] = c
out[1] = s
out[2] = 0
out[3] = 0
out[4] = -s
out[5] = c
out[6] = 0
out[7] = 0
out[8] = 0
out[9] = 0
out[10] = 1
out[11] = 0
out[12] = 0
out[13] = 0
out[14] = 0
out[15] = 1
return out
}
/**
* Generates a frustum matrix with the given bounds
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {Number} left Left bound of the frustum
* @param {Number} right Right bound of the frustum
* @param {Number} bottom Bottom bound of the frustum
* @param {Number} top Top bound of the frustum
* @param {Number} near Near bound of the frustum
* @param {Number} far Far bound of the frustum
* @returns {mat4} out
*/
function mat4frustum(out, left, right, bottom, top, near, far) {
var rl = 1 / (right - left),
tb = 1 / (top - bottom),
nf = 1 / (near - far);
out[0] = (near * 2) * rl;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = (near * 2) * tb;
out[6] = 0;
out[7] = 0;
out[8] = (right + left) * rl;
out[9] = (top + bottom) * tb;
out[10] = (far + near) * nf;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[14] = (far * near * 2) * nf;
out[15] = 0;
return out;
};
/**
* Set a mat4 to the identity matrix
*
* @param {mat4} out the receiving matrix
* @returns {mat4} out
*/
function mat4identity(out) {
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
};
/**
* Inverts a mat4
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the source matrix
* @returns {mat4} out
*/
function mat4invert(out, a) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
b00 = a00 * a11 - a01 * a10,
b01 = a00 * a12 - a02 * a10,
b02 = a00 * a13 - a03 * a10,
b03 = a01 * a12 - a02 * a11,
b04 = a01 * a13 - a03 * a11,
b05 = a02 * a13 - a03 * a12,
b06 = a20 * a31 - a21 * a30,
b07 = a20 * a32 - a22 * a30,
b08 = a20 * a33 - a23 * a30,
b09 = a21 * a32 - a22 * a31,
b10 = a21 * a33 - a23 * a31,
b11 = a22 * a33 - a23 * a32,
// Calculate the determinant
det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (!det) {
return null;
}
det = 1.0 / det;
out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
return out;
};
/**
* Generates a look-at matrix with the given eye position, focal point, and up axis
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {vec3} eye Position of the viewer
* @param {vec3} center Point the viewer is looking at
* @param {vec3} up vec3 pointing up
* @returns {mat4} out
*/
function mat4lookAt(out, eye, center, up) {
var x0, x1, x2, y0, y1, y2, z0, z1, z2, len,
eyex = eye[0],
eyey = eye[1],
eyez = eye[2],
upx = up[0],
upy = up[1],
upz = up[2],
centerx = center[0],
centery = center[1],
centerz = center[2];
if (Math.abs(eyex - centerx) < 0.000001 &&
Math.abs(eyey - centery) < 0.000001 &&
Math.abs(eyez - centerz) < 0.000001) {
return mat4identity(out);
}
z0 = eyex - centerx;
z1 = eyey - centery;
z2 = eyez - centerz;
len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
z0 *= len;
z1 *= len;
z2 *= len;
x0 = upy * z2 - upz * z1;
x1 = upz * z0 - upx * z2;
x2 = upx * z1 - upy * z0;
len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
if (!len) {
x0 = 0;
x1 = 0;
x2 = 0;
} else {
len = 1 / len;
x0 *= len;
x1 *= len;
x2 *= len;
}
y0 = z1 * x2 - z2 * x1;
y1 = z2 * x0 - z0 * x2;
y2 = z0 * x1 - z1 * x0;
len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
if (!len) {
y0 = 0;
y1 = 0;
y2 = 0;
} else {
len = 1 / len;
y0 *= len;
y1 *= len;
y2 *= len;
}
out[0] = x0;
out[1] = y0;
out[2] = z0;
out[3] = 0;
out[4] = x1;
out[5] = y1;
out[6] = z1;
out[7] = 0;
out[8] = x2;
out[9] = y2;
out[10] = z2;
out[11] = 0;
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
out[15] = 1;
return out;
};
/**
* Multiplies two mat4's
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the first operand
* @param {mat4} b the second operand
* @returns {mat4} out
*/
function mat4multiply(out, a, b) {
var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
// Cache only the current line of the second matrix
var b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
return out;
};
/**
* Generates a orthogonal projection matrix with the given bounds
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {number} left Left bound of the frustum
* @param {number} right Right bound of the frustum
* @param {number} bottom Bottom bound of the frustum
* @param {number} top Top bound of the frustum
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {mat4} out
*/
function mat4ortho(out, left, right, bottom, top, near, far) {
var lr = 1 / (left - right),
bt = 1 / (bottom - top),
nf = 1 / (near - far);
out[0] = -2 * lr;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = -2 * bt;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 2 * nf;
out[11] = 0;
out[12] = (left + right) * lr;
out[13] = (top + bottom) * bt;
out[14] = (far + near) * nf;
out[15] = 1;
return out;
};
/**
* Generates a perspective projection matrix with the given bounds
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {number} fovy Vertical field of view in radians
* @param {number} aspect Aspect ratio. typically viewport width/height
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {mat4} out
*/
function mat4perspective(out, fovy, aspect, near, far) {
var f = 1.0 / Math.tan(fovy / 2),
nf = 1 / (near - far);
out[0] = f / aspect;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = f;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = (far + near) * nf;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[14] = (2 * far * near) * nf;
out[15] = 0;
return out;
};
/**
* Generates a perspective projection matrix with the given field of view.
* This is primarily useful for generating projection matrices to be used
* with the still experiemental WebVR API.
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {number} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {mat4} out
*/
function mat4perspectiveFromFieldOfView(out, fov, near, far) {
var upTan = Math.tan(fov.upDegrees * Math.PI/180.0),
downTan = Math.tan(fov.downDegrees * Math.PI/180.0),
leftTan = Math.tan(fov.leftDegrees * Math.PI/180.0),
rightTan = Math.tan(fov.rightDegrees * Math.PI/180.0),
xScale = 2.0 / (leftTan + rightTan),
yScale = 2.0 / (upTan + downTan);
out[0] = xScale;
out[1] = 0.0;
out[2] = 0.0;
out[3] = 0.0;
out[4] = 0.0;
out[5] = yScale;
out[6] = 0.0;
out[7] = 0.0;
out[8] = -((leftTan - rightTan) * xScale * 0.5);
out[9] = ((upTan - downTan) * yScale * 0.5);
out[10] = far / (near - far);
out[11] = -1.0;
out[12] = 0.0;
out[13] = 0.0;
out[14] = (far * near) / (near - far);
out[15] = 0.0;
return out;
}
/**
* Rotates a mat4 by the given angle
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @param {vec3} axis the axis to rotate around
* @returns {mat4} out
*/
function mat4rotate(out, a, rad, axis) {
var x = axis[0], y = axis[1], z = axis[2],
len = Math.sqrt(x * x + y * y + z * z),
s, c, t,
a00, a01, a02, a03,
a10, a11, a12, a13,
a20, a21, a22, a23,
b00, b01, b02,
b10, b11, b12,
b20, b21, b22;
if (Math.abs(len) < 0.000001) { return null; }
len = 1 / len;
x *= len;
y *= len;
z *= len;
s = Math.sin(rad);
c = Math.cos(rad);
t = 1 - c;
a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
// Construct the elements of the rotation matrix
b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s;
b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s;
b20 = x * z * t + y * s; b21 = y * z * t - x * s; b22 = z * z * t + c;
// Perform rotation-specific matrix multiplication
out[0] = a00 * b00 + a10 * b01 + a20 * b02;
out[1] = a01 * b00 + a11 * b01 + a21 * b02;
out[2] = a02 * b00 + a12 * b01 + a22 * b02;
out[3] = a03 * b00 + a13 * b01 + a23 * b02;
out[4] = a00 * b10 + a10 * b11 + a20 * b12;
out[5] = a01 * b10 + a11 * b11 + a21 * b12;
out[6] = a02 * b10 + a12 * b11 + a22 * b12;
out[7] = a03 * b10 + a13 * b11 + a23 * b12;
out[8] = a00 * b20 + a10 * b21 + a20 * b22;
out[9] = a01 * b20 + a11 * b21 + a21 * b22;
out[10] = a02 * b20 + a12 * b21 + a22 * b22;
out[11] = a03 * b20 + a13 * b21 + a23 * b22;
if (a !== out) { // If the source and destination differ, copy the unchanged last row
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
return out;
};
/**
* Rotates a matrix by the given angle around the X axis
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4rotateX(out, a, rad) {
var s = Math.sin(rad),
c = Math.cos(rad),
a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7],
a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
if (a !== out) { // If the source and destination differ, copy the unchanged rows
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
// Perform axis-specific matrix multiplication
out[4] = a10 * c + a20 * s;
out[5] = a11 * c + a21 * s;
out[6] = a12 * c + a22 * s;
out[7] = a13 * c + a23 * s;
out[8] = a20 * c - a10 * s;
out[9] = a21 * c - a11 * s;
out[10] = a22 * c - a12 * s;
out[11] = a23 * c - a13 * s;
return out;
};
/**
* Rotates a matrix by the given angle around the Y axis
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4rotateY(out, a, rad) {
var s = Math.sin(rad),
c = Math.cos(rad),
a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3],
a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
if (a !== out) { // If the source and destination differ, copy the unchanged rows
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
// Perform axis-specific matrix multiplication
out[0] = a00 * c - a20 * s;
out[1] = a01 * c - a21 * s;
out[2] = a02 * c - a22 * s;
out[3] = a03 * c - a23 * s;
out[8] = a00 * s + a20 * c;
out[9] = a01 * s + a21 * c;
out[10] = a02 * s + a22 * c;
out[11] = a03 * s + a23 * c;
return out;
};
/**
* Rotates a matrix by the given angle around the Z axis
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
function mat4rotateZ(out, a, rad) {
var s = Math.sin(rad),
c = Math.cos(rad),
a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3],
a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7];
if (a !== out) { // If the source and destination differ, copy the unchanged last row
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
// Perform axis-specific matrix multiplication
out[0] = a00 * c + a10 * s;
out[1] = a01 * c + a11 * s;
out[2] = a02 * c + a12 * s;
out[3] = a03 * c + a13 * s;
out[4] = a10 * c - a00 * s;
out[5] = a11 * c - a01 * s;
out[6] = a12 * c - a02 * s;
out[7] = a13 * c - a03 * s;
return out;
};
/**
* Scales the mat4 by the dimensions in the given vec3
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to scale
* @param {vec3} v the vec3 to scale the matrix by
* @returns {mat4} out
**/
function mat4scale(out, a, v) {
var x = v[0], y = v[1], z = v[2];
out[0] = a[0] * x;
out[1] = a[1] * x;
out[2] = a[2] * x;
out[3] = a[3] * x;
out[4] = a[4] * y;
out[5] = a[5] * y;
out[6] = a[6] * y;
out[7] = a[7] * y;
out[8] = a[8] * z;
out[9] = a[9] * z;
out[10] = a[10] * z;
out[11] = a[11] * z;
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
};
/**
* Returns a string representation of a mat4
*
* @param {mat4} mat matrix to represent as a string
* @returns {String} string representation of the matrix
*/
function mat4str(a) {
return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' +
a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' +
a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' +
a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')';
};
/**
* Translate a mat4 by the given vector
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the matrix to translate
* @param {vec3} v vector to translate by
* @returns {mat4} out
*/
function mat4translate(out, a, v) {
var x = v[0], y = v[1], z = v[2],
a00, a01, a02, a03,
a10, a11, a12, a13,
a20, a21, a22, a23;
if (a === out) {
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
} else {
a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;
out[12] = a00 * x + a10 * y + a20 * z + a[12];
out[13] = a01 * x + a11 * y + a21 * z + a[13];
out[14] = a02 * x + a12 * y + a22 * z + a[14];
out[15] = a03 * x + a13 * y + a23 * z + a[15];
}
return out;
};
/**
* Transpose the values of a mat4
*
* @param {mat4} out the receiving matrix
* @param {mat4} a the source matrix
* @returns {mat4} out
*/
function mat4transpose(out, a) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (out === a) {
var a01 = a[1], a02 = a[2], a03 = a[3],
a12 = a[6], a13 = a[7],
a23 = a[11];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a01;
out[6] = a[9];
out[7] = a[13];
out[8] = a02;
out[9] = a12;
out[11] = a[14];
out[12] = a03;
out[13] = a13;
out[14] = a23;
} else {
out[0] = a[0];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a[1];
out[5] = a[5];
out[6] = a[9];
out[7] = a[13];
out[8] = a[2];
out[9] = a[6];
out[10] = a[10];
out[11] = a[14];
out[12] = a[3];
out[13] = a[7];
out[14] = a[11];
out[15] = a[15];
}
return out;
};
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.