the Cold Dark: Help: Objects: Math Library

Core Help Root: Objects: Math Library

.add(v1,v2) native: Vector addition. It adds two floating-point lists, element-by-element.
.sub(v1,v2) native: Vector substraction.
.dot(v1,v2) native: Dot product of two vectors.
.cross(v1,v2) native: Cross product of 3-dimensional vectors.
.distance(v1,v2) native: Euclidean distance between the two vectors.
.scale(x,v) native: Scales the vector v by scalar x.
.minor(v1,v2) native: Calculates element-by-element minimum of the two lists. Used for boxes.
.major(v1,v2) native: Calculates element-by-element maximum.
.is_lower(v1,v2) native: Returns true if every element of v1 is lesser or equal than corresponding element of v2.

.pi(): Returns pi.
.pi2(): Returns 2*pi.
.deg_rad(angle): Converts the angle from degrees to radians.
.rad_deg(angle): Converts the angle from radians to degrees.
.polar_rectangular(coords): Transforms pair [distance, angle] into [x,y].
.rectangular_polar(coords): Inverse of the above.
.cylindrical_rectangular(coords): Transforms [r, angle, z] into [x,y,z].
.rectangular_cylindrical(coords): Inverse of the above.
.spherical_rectangular(coords): Transform [r, phi, theta] into [x,y,z].
.rectangular_spherical(coords): Inverse of the above.

.matrix_add(m1,m2): Add two matrices.
.matrix_sub(m1,m2): Substract m2 from m1
.matrix_mul(m1,m2): Multiply the two matrices (their dimensions must be compatible for multiplication, of course)
.matrix_scale(s,m): Scale the matrix m by scalar s.
.transpose(m): Transpose the matrix. This will actually work regardless of the element type, so the operation is useful on lists, as well.
.ident_mat(n): Returns n-dimensional identity matrix.
.translation_mat(v): Constructs the matrix for translation by vector v. It works for 2d or 3d case.
.tensor(m1,m2): Tensor product of the two vectors. This is the matrix A with the property that Ax=<x,v1>v2.
.skew(v): Construct a skew operator for the vector v. That's matrix A that turns any vector into its cross product with v. This is used by rotation_mat_3d.
.rotation_mat_2d(angle): Construct 2d rotation matrix for the given angle.
.rotation_mat_3d(axis,angle): This is 3d rotation. Valid values for axis are 'x, 'y, 'z, or a 3d vector. The result is a homogenous matrix.
.scale_mat(scale): Returns a scaling matrix (nonuniform). Scale is assumed to be 2d or 3d vector.
.transform_vect(m,v): Transform the vector by matrix. This will work for both normal and homogenous matrices (determined by comparing the dimensions of the matrix and vector).

.runge(x,y,h,f,data): This is one step in Runge-Kutta method for ordinary differential equations. Scalar x and vector y are the current values of independant and dependant variables, h is the timestep, f is the method on the sender that accepts x, y, and data, and returns the right-hand-side of the equation.