30:T8ae,/** * 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; };31:T89f,/** * 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)) ); }32:T44d,/** * 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 }33:T4ac,/** * 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; };34:T79c,/** * 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; };35:T7c1,/** * 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; };36:T5da,/** * 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; };37:T523,/** * 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; }38:T7ef,/** * 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; };39:T44b,/** * 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; };3a:T44b,/** * 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; };3b:T44d,/** * 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; };3c:T4d7,/** * 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; };3d:T44f,/** * 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; };3e:[] 2e:{"title":"gl-mat4","cells":[{"id":0,"value":"md`# gl-mat4`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"md`This notebook re-exports functions from [stackgl/gl-mat4](https://github.com/stackgl/gl-mat4). The license may be found [here](https://github.com/stackgl/gl-mat4/blob/master/LICENSE.md).\n\nAdditionally, it adds a function called \\`mat4fromMat3\\` to expand a 2d homogeneous transformation matrix to a 3d homogeneous transformation matrix.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":6,"value":"md`## License\n\nCopyright (c) 2013 Brandon Jones, Colin MacKenzie IV\n\nThis software is provided 'as-is', without any express or implied\nwarranty. In no event will the authors be held liable for any damages\narising from the use of this software.\n\nPermission is granted to anyone to use this software for any purpose,\nincluding commercial applications, and to alter it and redistribute it\nfreely, subject to the following restrictions:\n\n 1. The origin of this software must not be misrepresented you must not\n claim that you wrote the original software. If you use this software\n in a product, an acknowledgment in the product documentation would be\n appreciated but is not required.\n\n 2. Altered source versions must be plainly marked as such, and must not\n be misrepresented as being the original software.\n\n 3. This notice may not be removed or altered from any source distribution.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"md`## Usage\n\nThere are two basic ways to use this module. You may either import all functions\n\n\\`\\`\\`js\nimport {mat4} from '@rreusser/gl-mat4'\n\\`\\`\\`\n\nafter which you can use the functions like normal, e.g.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"a = mat4.create()","pinned":true,"hidden":false,"mode":"ojs"},{"id":17,"value":"md`\nor you may import single functions directly\n\n\\`\\`\\`js\nimport {mat4create} from '@rreusser/gl-mat4'\n\\`\\`\\`\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"b = mat4create()","pinned":true,"hidden":false,"mode":"ojs"},{"id":23,"value":"md`## Implementation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":84,"value":"mat4 = ({\n EPSILON,\n equals: mat4equals,\n create: mat4create,\n clone: mat4clone,\n copy: mat4copy,\n identity: mat4identity,\n transpose: mat4transpose,\n invert: mat4invert,\n adjoint: mat4adjoint,\n determinant: mat4determinant,\n multiply: mat4multiply,\n translate: mat4translate,\n scale: mat4scale,\n rotate: mat4rotate,\n rotateX: mat4rotateX,\n rotateY: mat4rotateY,\n rotateZ: mat4rotateZ,\n fromMat3: mat4fromMat3,\n fromRotation: mat4fromRotation,\n fromRotationTranslation: mat4fromRotationTranslation,\n fromScaling: mat4fromScaling,\n fromTranslation: mat4fromTranslation,\n fromXRotation: mat4fromXRotation,\n fromYRotation: mat4fromYRotation,\n fromZRotation: mat4fromZRotation,\n fromQuat: mat4fromQuat,\n frustum: mat4frustum,\n perspective: mat4perspective,\n perspectiveFromFieldOfView: mat4perspectiveFromFieldOfView,\n ortho: mat4ortho,\n lookAt: mat4lookAt,\n str: mat4str\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":140,"value":"EPSILON = 0.000001","pinned":true,"hidden":false,"mode":"ojs"},{"id":25,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":26,"value":"/**\n * Creates a new mat4 initialized with values from an existing matrix\n *\n * @param {mat4} a matrix to clone\n * @returns {mat4} a new 4x4 matrix\n */\nfunction mat4clone(a) {\n var out = new Float32Array(16);\n out[0] = a[0];\n out[1] = a[1];\n out[2] = a[2];\n out[3] = a[3];\n out[4] = a[4];\n out[5] = a[5];\n out[6] = a[6];\n out[7] = a[7];\n out[8] = a[8];\n out[9] = a[9];\n out[10] = a[10];\n out[11] = a[11];\n out[12] = a[12];\n out[13] = a[13];\n out[14] = a[14];\n out[15] = a[15];\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":28,"value":"/**\n * Copy the values from one mat4 to another\n *\n * @param {mat4} out the receiving matrix\n * @param {mat4} a the source matrix\n * @returns {mat4} out\n */\nfunction mat4copy(out, a) {\n out[0] = a[0];\n out[1] = a[1];\n out[2] = a[2];\n out[3] = a[3];\n out[4] = a[4];\n out[5] = a[5];\n out[6] = a[6];\n out[7] = a[7];\n out[8] = a[8];\n out[9] = a[9];\n out[10] = a[10];\n out[11] = a[11];\n out[12] = a[12];\n out[13] = a[13];\n out[14] = a[14];\n out[15] = a[15];\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":134,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":30,"value":"/**\n * Creates a new identity mat4\n *\n * @returns {mat4} a new 4x4 matrix\n */\nfunction mat4create() {\n var out = new Float32Array(16);\n out[0] = 1;\n out[1] = 0;\n out[2] = 0;\n out[3] = 0;\n out[4] = 0;\n out[5] = 1;\n out[6] = 0;\n out[7] = 0;\n out[8] = 0;\n out[9] = 0;\n out[10] = 1;\n out[11] = 0;\n out[12] = 0;\n out[13] = 0;\n out[14] = 0;\n out[15] = 1;\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":32,"value":"/**\n * Calculates the determinant of a mat4\n *\n * @param {mat4} a the source matrix\n * @returns {Number} determinant of a\n */\nfunction mat4determinant(a) {\n var a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],\n a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],\n a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],\n a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],\n\n b00 = a00 * a11 - a01 * a10,\n b01 = a00 * a12 - a02 * a10,\n b02 = a00 * a13 - a03 * a10,\n b03 = a01 * a12 - a02 * a11,\n b04 = a01 * a13 - a03 * a11,\n b05 = a02 * a13 - a03 * a12,\n b06 = a20 * a31 - a21 * a30,\n b07 = a20 * a32 - a22 * a30,\n b08 = a20 * a33 - a23 * a30,\n b09 = a21 * a32 - a22 * a31,\n b10 = a21 * a33 - a23 * a31,\n b11 = a22 * a33 - a23 * a32;\n\n // Calculate the determinant\n return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":34,"value":"/**\n * Creates a matrix from a quaternion rotation.\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {quat4} q Rotation quaternion\n * @returns {mat4} out\n */\nfunction mat4fromQuat(out, q) {\n var x = q[0], y = q[1], z = q[2], w = q[3],\n x2 = x + x,\n y2 = y + y,\n z2 = z + z,\n\n xx = x * x2,\n yx = y * x2,\n yy = y * y2,\n zx = z * x2,\n zy = z * y2,\n zz = z * z2,\n wx = w * x2,\n wy = w * y2,\n wz = w * z2;\n\n out[0] = 1 - yy - zz;\n out[1] = yx + wz;\n out[2] = zx - wy;\n out[3] = 0;\n\n out[4] = yx - wz;\n out[5] = 1 - xx - zz;\n out[6] = zy + wx;\n out[7] = 0;\n\n out[8] = zx + wy;\n out[9] = zy - wx;\n out[10] = 1 - xx - yy;\n out[11] = 0;\n\n out[12] = 0;\n out[13] = 0;\n out[14] = 0;\n out[15] = 1;\n\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":38,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"id":116,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"},{"id":126,"value":"/**\n * Creates a matrix from a 2d homogeneous transformation matrix. The\n * z component receives the identity matrix components.\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {mat3} a input transformation matrix\n * @returns {mat4} out\n */\nfunction mat4fromMat3 (out, a) {\n out[0] = a[0]\n out[1] = a[1]\n out[2] = 0\n out[3] = a[2]\n \n out[4] = a[3]\n out[5] = a[4]\n out[6] = 0\n out[7] = a[5]\n \n out[8] = 0\n out[9] = 0\n out[10] = 1\n out[11] = 0\n \n out[12] = a[6]\n out[13] = a[7]\n out[14] = 0\n out[15] = a[8]\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":40,"value":"/**\n * Creates a matrix from a vector scaling\n * This is equivalent to (but much faster than):\n *\n * mat4.identity(dest)\n * mat4.scale(dest, dest, vec)\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {vec3} v Scaling vector\n * @returns {mat4} out\n */\nfunction mat4fromScaling(out, v) {\n out[0] = v[0]\n out[1] = 0\n out[2] = 0\n out[3] = 0\n out[4] = 0\n out[5] = v[1]\n out[6] = 0\n out[7] = 0\n out[8] = 0\n out[9] = 0\n out[10] = v[2]\n out[11] = 0\n out[12] = 0\n out[13] = 0\n out[14] = 0\n out[15] = 1\n return out\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":42,"value":"/**\n * Creates a matrix from a vector translation\n * This is equivalent to (but much faster than):\n *\n * mat4.identity(dest)\n * mat4.translate(dest, dest, vec)\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {vec3} v Translation vector\n * @returns {mat4} out\n */\nfunction mat4fromTranslation(out, v) {\n out[0] = 1\n out[1] = 0\n out[2] = 0\n out[3] = 0\n out[4] = 0\n out[5] = 1\n out[6] = 0\n out[7] = 0\n out[8] = 0\n out[9] = 0\n out[10] = 1\n out[11] = 0\n out[12] = v[0]\n out[13] = v[1]\n out[14] = v[2]\n out[15] = 1\n return out\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":44,"value":"/**\n * Creates a matrix from the given angle around the X axis\n * This is equivalent to (but much faster than):\n *\n * mat4.identity(dest)\n * mat4.rotateX(dest, dest, rad)\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {Number} rad the angle to rotate the matrix by\n * @returns {mat4} out\n */\nfunction mat4fromXRotation(out, rad) {\n var s = Math.sin(rad),\n c = Math.cos(rad)\n\n // Perform axis-specific matrix multiplication\n out[0] = 1\n out[1] = 0\n out[2] = 0\n out[3] = 0\n out[4] = 0\n out[5] = c\n out[6] = s\n out[7] = 0\n out[8] = 0\n out[9] = -s\n out[10] = c\n out[11] = 0\n out[12] = 0\n out[13] = 0\n out[14] = 0\n out[15] = 1\n return out\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":46,"value":"/**\n * Creates a matrix from the given angle around the Y axis\n * This is equivalent to (but much faster than):\n *\n * mat4.identity(dest)\n * mat4.rotateY(dest, dest, rad)\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {Number} rad the angle to rotate the matrix by\n * @returns {mat4} out\n */\nfunction mat4fromYRotation(out, rad) {\n var s = Math.sin(rad),\n c = Math.cos(rad)\n\n // Perform axis-specific matrix multiplication\n out[0] = c\n out[1] = 0\n out[2] = -s\n out[3] = 0\n out[4] = 0\n out[5] = 1\n out[6] = 0\n out[7] = 0\n out[8] = s\n out[9] = 0\n out[10] = c\n out[11] = 0\n out[12] = 0\n out[13] = 0\n out[14] = 0\n out[15] = 1\n return out\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":48,"value":"/**\n * Creates a matrix from the given angle around the Z axis\n * This is equivalent to (but much faster than):\n *\n * mat4.identity(dest)\n * mat4.rotateZ(dest, dest, rad)\n *\n * @param {mat4} out mat4 receiving operation result\n * @param {Number} rad the angle to rotate the matrix by\n * @returns {mat4} out\n */\nfunction mat4fromZRotation(out, rad) {\n var s = Math.sin(rad),\n c = Math.cos(rad)\n\n // Perform axis-specific matrix multiplication\n out[0] = c\n out[1] = s\n out[2] = 0\n out[3] = 0\n out[4] = -s\n out[5] = c\n out[6] = 0\n out[7] = 0\n out[8] = 0\n out[9] = 0\n out[10] = 1\n out[11] = 0\n out[12] = 0\n out[13] = 0\n out[14] = 0\n out[15] = 1\n return out\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":50,"value":"/**\n * Generates a frustum matrix with the given bounds\n *\n * @param {mat4} out mat4 frustum matrix will be written into\n * @param {Number} left Left bound of the frustum\n * @param {Number} right Right bound of the frustum\n * @param {Number} bottom Bottom bound of the frustum\n * @param {Number} top Top bound of the frustum\n * @param {Number} near Near bound of the frustum\n * @param {Number} far Far bound of the frustum\n * @returns {mat4} out\n */\nfunction mat4frustum(out, left, right, bottom, top, near, far) {\n var rl = 1 / (right - left),\n tb = 1 / (top - bottom),\n nf = 1 / (near - far);\n out[0] = (near * 2) * rl;\n out[1] = 0;\n out[2] = 0;\n out[3] = 0;\n out[4] = 0;\n out[5] = (near * 2) * tb;\n out[6] = 0;\n out[7] = 0;\n out[8] = (right + left) * rl;\n out[9] = (top + bottom) * tb;\n out[10] = (far + near) * nf;\n out[11] = -1;\n out[12] = 0;\n out[13] = 0;\n out[14] = (far * near * 2) * nf;\n out[15] = 0;\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":52,"value":"/**\n * Set a mat4 to the identity matrix\n *\n * @param {mat4} out the receiving matrix\n * @returns {mat4} out\n */\nfunction mat4identity(out) {\n out[0] = 1;\n out[1] = 0;\n out[2] = 0;\n out[3] = 0;\n out[4] = 0;\n out[5] = 1;\n out[6] = 0;\n out[7] = 0;\n out[8] = 0;\n out[9] = 0;\n out[10] = 1;\n out[11] = 0;\n out[12] = 0;\n out[13] = 0;\n out[14] = 0;\n out[15] = 1;\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":54,"value":"$34","pinned":true,"hidden":false,"mode":"ojs"},{"id":56,"value":"$35","pinned":true,"hidden":false,"mode":"ojs"},{"id":58,"value":"$36","pinned":true,"hidden":false,"mode":"ojs"},{"id":60,"value":"/**\n * Generates a orthogonal projection matrix with the given bounds\n *\n * @param {mat4} out mat4 frustum matrix will be written into\n * @param {number} left Left bound of the frustum\n * @param {number} right Right bound of the frustum\n * @param {number} bottom Bottom bound of the frustum\n * @param {number} top Top bound of the frustum\n * @param {number} near Near bound of the frustum\n * @param {number} far Far bound of the frustum\n * @returns {mat4} out\n */\nfunction mat4ortho(out, left, right, bottom, top, near, far) {\n var lr = 1 / (left - right),\n bt = 1 / (bottom - top),\n nf = 1 / (near - far);\n out[0] = -2 * lr;\n out[1] = 0;\n out[2] = 0;\n out[3] = 0;\n out[4] = 0;\n out[5] = -2 * bt;\n out[6] = 0;\n out[7] = 0;\n out[8] = 0;\n out[9] = 0;\n out[10] = 2 * nf;\n out[11] = 0;\n out[12] = (left + right) * lr;\n out[13] = (top + bottom) * bt;\n out[14] = (far + near) * nf;\n out[15] = 1;\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":62,"value":"/**\n * Generates a perspective projection matrix with the given bounds\n *\n * @param {mat4} out mat4 frustum matrix will be written into\n * @param {number} fovy Vertical field of view in radians\n * @param {number} aspect Aspect ratio. typically viewport width/height\n * @param {number} near Near bound of the frustum\n * @param {number} far Far bound of the frustum\n * @returns {mat4} out\n */\nfunction mat4perspective(out, fovy, aspect, near, far) {\n var f = 1.0 / Math.tan(fovy / 2),\n nf = 1 / (near - far);\n out[0] = f / aspect;\n out[1] = 0;\n out[2] = 0;\n out[3] = 0;\n out[4] = 0;\n out[5] = f;\n out[6] = 0;\n out[7] = 0;\n out[8] = 0;\n out[9] = 0;\n out[10] = (far + near) * nf;\n out[11] = -1;\n out[12] = 0;\n out[13] = 0;\n out[14] = (2 * far * near) * nf;\n out[15] = 0;\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":64,"value":"$37","pinned":true,"hidden":false,"mode":"ojs"},{"id":66,"value":"$38","pinned":true,"hidden":false,"mode":"ojs"},{"id":68,"value":"$39","pinned":true,"hidden":false,"mode":"ojs"},{"id":70,"value":"$3a","pinned":true,"hidden":false,"mode":"ojs"},{"id":72,"value":"$3b","pinned":true,"hidden":false,"mode":"ojs"},{"id":74,"value":"/**\n * Scales the mat4 by the dimensions in the given vec3\n *\n * @param {mat4} out the receiving matrix\n * @param {mat4} a the matrix to scale\n * @param {vec3} v the vec3 to scale the matrix by\n * @returns {mat4} out\n **/\nfunction mat4scale(out, a, v) {\n var x = v[0], y = v[1], z = v[2];\n\n out[0] = a[0] * x;\n out[1] = a[1] * x;\n out[2] = a[2] * x;\n out[3] = a[3] * x;\n out[4] = a[4] * y;\n out[5] = a[5] * y;\n out[6] = a[6] * y;\n out[7] = a[7] * y;\n out[8] = a[8] * z;\n out[9] = a[9] * z;\n out[10] = a[10] * z;\n out[11] = a[11] * z;\n out[12] = a[12];\n out[13] = a[13];\n out[14] = a[14];\n out[15] = a[15];\n return out;\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":76,"value":"/**\n * Returns a string representation of a mat4\n *\n * @param {mat4} mat matrix to represent as a string\n * @returns {String} string representation of the matrix\n */\nfunction mat4str(a) {\n return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' +\n a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' +\n a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' + \n a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')';\n};","pinned":true,"hidden":false,"mode":"ojs"},{"id":78,"value":"$3c","pinned":true,"hidden":false,"mode":"ojs"},{"id":80,"value":"$3d","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W3e","stdlib":"1","titling":"auto"}