View Source Graphmath.Mat33 (graphmath v2.6.0)
This is the 3D mathematics.
This submodule handles 3x3 matrices using tuples of floats.
Summary
Functions
add(a,b)
adds one mat33
to another mat33
.
apply( a, v )
transforms a vec3
by a mat33
.
apply_left( v, a )
transforms a vec3
by a mat33
, applied on the left.
apply_left_transpose( v, a )
transforms a vec3
by a transposed mat33
, applied on the left.
apply_transpose( a, v )
transforms a vec3
by a a transposed mat33
.
at( a, i, j)
selects an element of a mat33
.
column0( a )
selects the first column of a mat33
.
column1( a )
selects the second column of a mat33
.
column2( a )
selects the third column of a mat33
.
diag( a )
selects the diagonal of a mat33
.
identity()
creates an identity mat33
.
inverse(a)
calculates the inverse matrix
make_rotate( theta )
creates a mat33 that rotates a vec2 by theta
radians about the +Z axis.
make_scale( k )
creates a mat33
that uniformly scales.
make_scale( sx, sy, sz )
creates a mat33
that scales each axis independently.
make_translate( tx, ty )
creates a mat33 that translates a vec2 by (tx, ty).
multiply( a, b )
multiply two matrices a and b together.
multiply_transpose( a, b )
multiply two matrices a and b<sup>T</sup> together.
round( a, sigfigs )
rounds every element of a mat33
to some number of decimal places.
row0( a )
selects the first row of a mat33
.
row1( a )
selects the second row of a mat33
.
row2( a )
selects the third row of a mat33
.
scale( a, k )
scales every element in a mat33
by a coefficient k.
subtract(a,b)
subtracts one mat33
from another mat33
.
transform_point( a, v )
transforms a vec2
point by a mat33
.
transform_vector( a, v )
transforms a vec2
vector by a mat33
.
zero()
creates a zeroed mat33
.
Types
Functions
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
.
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.
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.
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**<sup>T</sup>.
This is the "full" application of a matrix, and uses all elements.
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<sup>T</sup>v.
This is the "full" application of a matrix, and uses all elements.
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
.
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
.
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
.
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
.
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
.
inverse(a)
calculates the inverse matrix
a
is a mat33
to be inverted
Returs a mat33
representing a
<sup>-1</sup>
Raises an error when you try to calculate inverse of a matrix whose determinant is zero
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.
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 k
s.
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 vec2
s via the transform methods, sz
will have no effect.
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 }
.
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
.
multiply_transpose( a, b )
multiply two matrices a and b<sup>T</sup> together.
a
is the mat33
multiplicand.
b
is the mat33
multiplier.
This returns the mat33
product of the a
and b
<sup>T</sup>.
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
.
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
.
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
.
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
.
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
.
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
.
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.
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
.