@spec add(mat33(), mat33()) :: mat33()

add(a,b) adds one mat33 to another mat33.

a is the first mat33.

b is the second mat33.

This returns a mat33 which is the element-wise sum of a and b.

@spec apply(mat33(), vec3()) :: vec3()

apply( a, v ) transforms a vec3 by a mat33.

a is the mat33 to transform by.

v is the vec3 to be transformed.

This returns a vec3 representing A**v**.

This is the "full" application of a matrix, and uses all elements.

@spec apply_left(vec3(), mat33()) :: vec3()

apply_left( v, a ) transforms a vec3 by a mat33, applied on the left.

a is the mat33 to transform by.

v is the vec3 to be transformed.

This returns a vec3 representing v**A**.

This is the "full" application of a matrix, and uses all elements.

@spec apply_left_transpose(vec3(), mat33()) :: vec3()

apply_left_transpose( v, a ) transforms a vec3 by a transposed mat33, applied on the left.

a is the mat33 to transform by.

v is the vec3 to be transformed.

This returns a vec3 representing v**A**^T.

This is the "full" application of a matrix, and uses all elements.

@spec apply_transpose(mat33(), vec3()) :: vec3()

apply_transpose( a, v ) transforms a vec3 by a a transposed mat33.

a is the mat33 to transform by.

v is the vec3 to be transformed.

This returns a vec3 representing A^Tv.

This is the "full" application of a matrix, and uses all elements.

@spec at(mat33(), 0..2, 0..2) :: float()

at( a, i, j) selects an element of a mat33.

a is the mat33 to index.

i is the row integer index [0,2].

j is the column integer index [0,2].

This returns a float from the matrix at row i and column j.

@spec column0(mat33()) :: vec3()

column0( a ) selects the first column of a mat33.

a is the mat33 to take the first column of.

This returns a vec3 representing the first column of a.

@spec column1(mat33()) :: vec3()

column1( a ) selects the second column of a mat33.

a is the mat33 to take the second column of.

This returns a vec3 representing the second column of a.

@spec column2(mat33()) :: vec3()

column2( a ) selects the third column of a mat33.

a is the mat33 to take the third column of.

This returns a vec3 representing the third column of a.

@spec diag(mat33()) :: vec3()

diag( a ) selects the diagonal of a mat33.

a is the mat33 to take the diagonal of.

This returns a vec3 representing the diagonal of a.

@spec identity() :: mat33()

identity() creates an identity mat33.

This returns an identity mat33.

@spec inverse(mat33()) :: mat33()

inverse(a) calculates the inverse matrix

a is a mat33 to be inverted

Returs a mat33 representing a^-1

Raises an error when you try to calculate inverse of a matrix whose determinant is zero

@spec make_rotate(float()) :: mat33()

make_rotate( theta ) creates a mat33 that rotates a vec2 by theta radians about the +Z axis.

theta is the float of the number of radians of rotation the matrix will provide.

This returns a mat33 which rotates by theta radians about the +Z axis.

@spec make_scale(float()) :: mat33()

make_scale( k ) creates a mat33 that uniformly scales.

k is the float value to scale by.

This returns a mat33 whose diagonal is all ks.

@spec make_scale(float(), float(), float()) :: mat33()

make_scale( sx, sy, sz ) creates a mat33 that scales each axis independently.

sx is a float for scaling the x-axis.

sy is a float for scaling the y-axis.

sz is a float for scaling the z-axis.

This returns a mat33 whose diagonal is { sx, sy, sz }.

Note that, when used with vec2s via the transform methods, sz will have no effect.

@spec make_translate(float(), float()) :: mat33()

make_translate( tx, ty ) creates a mat33 that translates a vec2 by (tx, ty).

tx is a float for translating along the x-axis.

ty is a float for translating along the y-axis.

This returns a mat33 which translates by a vec2 { tx, ty }.

@spec multiply(mat33(), mat33()) :: mat33()

multiply( a, b ) multiply two matrices a and b together.

a is the mat33 multiplicand.

b is the mat33 multiplier.

This returns the mat33 product of the a and b.

@spec multiply_transpose(mat33(), mat33()) :: mat33()

multiply_transpose( a, b ) multiply two matrices a and b^T together.

a is the mat33 multiplicand.

b is the mat33 multiplier.

This returns the mat33 product of the a and b^T.

@spec round(mat33(), 0..15) :: mat33()

round( a, sigfigs ) rounds every element of a mat33 to some number of decimal places.

a is the mat33 to round.

sigfigs is an integer on [0,15] of the number of decimal places to round to.

This returns a mat33 which is the result of rounding a.

@spec row0(mat33()) :: vec3()

row0( a ) selects the first row of a mat33.

a is the mat33 to take the first row of.

This returns a vec3 representing the first row of a.

@spec row1(mat33()) :: vec3()

row1( a ) selects the second row of a mat33.

a is the mat33 to take the second row of.

This returns a vec3 representing the second row of a.

@spec row2(mat33()) :: vec3()

row2( a ) selects the third row of a mat33.

a is the mat33 to take the third row of.

This returns a vec3 representing the third row of a.

@spec scale(mat33(), float()) :: mat33()

scale( a, k ) scales every element in a mat33 by a coefficient k.

a is the mat33 to scale.

k is the float to scale by.

This returns a mat33 a scaled element-wise by k.

@spec subtract(mat33(), mat33()) :: mat33()

subtract(a,b) subtracts one mat33 from another mat33.

a is the minuend.

b is the subtraherd.

This returns a mat33 formed by the element-wise subtraction of b from a.

@spec transform_point(mat33(), vec2()) :: vec2()

transform_point( a, v ) transforms a vec2 point by a mat33.

a is a mat33 used to transform the point.

v is a vec2 to be transformed.

This returns a vec2 representing the application of a to v.

The point a is internally treated as having a third coordinate equal to 1.0.

Note that transforming a point will work for all transforms.

@spec transform_vector(mat33(), vec2()) :: vec2()

transform_vector( a, v ) transforms a vec2 vector by a mat33.

a is a mat33 used to transform the point.

v is a vec2 to be transformed.

This returns a vec2 representing the application of a to v.

The point a is internally treated as having a third coordinate equal to 0.0.

Note that transforming a vector will work for only rotations, scales, and shears.

@spec zero() :: mat33()

zero() creates a zeroed mat33.

This returns a zeroed mat33.