## gl-math

A small math library aimed at gamedev that provides 4x4 float matrix, vector, and quaternion operations. Uses the hypermath library.

• srfi-1
• matchable

### Documentation

gl-math provides a number of functions for working with 4x4 matrices (plus a handful of others). The functionality is similar to what can be found in the glm egg, but with some notable differences:

• Matrix functions only operate on 4x4 matrices
• Matrix functions can accept either f32vectors or pointers
• No container is used to represent matrices

Additionally, gl-math is one fifth the compiled size of glm, has a more straight-forward code-base, and complete documentation.

gl-math expects matrices, vectors, and quaternions to be f32vectors or pointers. f32vectors must be 16 elements long, 3 elements long, or 4 elements long for matrices, vectors, or quaternions, respectively. The memory pointed to should likewise be an array of 16, 3, or 4 floats . If a function accepts more than one matrix, vector, or quaternion, all must be of the same type.

gl-math operates on matrices in a column-major fashion in correspondence with OpenGL (e.g. translation components are at indices 12, 13, and 14). Vectors are arranged as ((x y z)), and quaternions as ((x y z w)).

#### Matrix operations

[procedure] (print-mat4 MATRIX)

Prints the given MATRIX to (current-output-port).

[procedure] (copy-mat4 MATRIX [RESULT])

Make a copy of MATRIX. If the matrix RESULT is given, it will be modified to contain the contents of MATRIX. If RESULT is #t, MATRIX must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, MATRIX must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (m* A B [RESULT])

Multiply matrix A with matrix B. If the matrix RESULT is given, it will be modified to contain the results of the multiplication. If RESULT is #t, A and B must be f32vectors and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, A and B must be f32vectors and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (m*s A S [RESULT])

Multiply matrix A by scalar S. If the matrix RESULT is given, it will be modified to contain the results of the multiplication. If RESULT is #t, A must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, A must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (m+ A B [RESULT])

Add matrix A by matrix B. If the matrix RESULT is given, it will be modified to contain the results of the multiplication. If RESULT is #t, A and B must be f32vectors and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, A and B must be f32vectors and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (m- A B [RESULT])

Subtract matrix B from matrix A. If the matrix RESULT is given, it will be modified to contain the results of the multiplication. If RESULT is #t, A and B must be f32vectors and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, A and B must be f32vectors and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (mat4-identity [RESULT])

Return an identity matrix. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (translation VECTOR [RESULT])

Return the translation matrix given by VECTOR. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (translate VECTOR MATRIX)

Translate MATRIX by VECTOR.

[procedure] (x-rotation ANGLE [RESULT])

Return the rotation matrix given by a rotation of ANGLE radians around the x-axis. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-x ANGLE MATRIX)

Rotate MATRIX around the x-axis by ANGLE radians.

[procedure] (y-rotation ANGLE [RESULT])

Return the rotation matrix given by a rotation of ANGLE radians around the y-axis. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-y ANGLE MATRIX)

Rotate MATRIX around the y-axis by ANGLE radians.

[procedure] (z-rotation ANGLE [RESULT])

Return the rotation matrix given by a rotation of ANGLE radians around the z-axis. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-z ANGLE MATRIX)

Rotate MATRIX around the z-axis by ANGLE radians.

[procedure] (axis-angle-rotation AXIS ANGLE [RESULT])

Return the rotation matrix given by a rotation of ANGLE radians around the vector AXIS. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-axis-angle AXIS ANGLE MATRIX)

Rotate MATRIX around the vector AXIS by ANGLE radians.

[procedure] (quaternion-rotation Q [RESULT])

Return the rotation matrix given by the quaternion Q. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-quaternion Q MATRIX)

Rotate MATRIX by the quaternion Q.

[procedure] (ypr-rotation YAW PITCH ROLL [RESULT])

Return the rotation matrix given by rotating by ROLL radians around the z-axis followed by PITCH radians around the x-axis followed by YAW radians around the y-axis. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (rotate-ypr YAW PITCH ROLL MATRIX)

Rotate MATRIX by ROLL radians around the z-axis followed by PITCH radians around the x-axis followed by YAW radians around the y-axis.

[procedure] (2d-scaling SCALE-X SCALE-Y [RESULT])

Return the matrix created by scaling the x and y axes by SCALE-X and SCALE-Y. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (scale-2d SCALE-X SCALE-Y MATRIX)

Scale the x and y axis of MATRIX by SCALE-X and SCALE-Y.

[procedure] (3d-scaling SCALE-X SCALE-Y SCALE-Z [RESULT])

Return the matrix created by scaling the x, y and z axes by SCALE-X, SCALE-Y, and SCALE-Z. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (scale-3d SCALE-X SCALE-Y SCALE-Z MATRIX)

Scale the x, y, and z axis of MATRIX by SCALE-X, SCALE-Y, and SCALE-Z.

[procedure] (scaling SCALE [RESULT])

Return the matrix created by scaling the x, y and z axes by SCALE. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (scale SCALE MATRIX)

Scale the x, y, and z axis of MATRIX by SCALE.

[procedure] (flip-x MATRIX)

Flip (mirror) MATRIX along the x-axis.

[procedure] (flip-y MATRIX)

Flip (mirror) MATRIX along the y-axis.

[procedure] (flip-z MATRIX)

Flip (mirror) MATRIX along the z-axis.

[procedure] (translate-rotate-scale-2d VECTOR ANGLE SCALE [RESULT])

Efficiently create a matrix translated by VECTOR, rotated around the z-axis by ANGLE radians, then scaled by SCALE. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (transpose MATRIX [RESULT])

Transpose MATRIX. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, MATRIX must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, MATRIX must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (inverse MATRIX [RESULT])

Invert MATRIX. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, MATRIX must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, MATRIX must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (fast-inverse-transpose MATRIX [RESULT])

Efficiently inverse the transpose the unscaled MATRIX. If MATRIX has been scaled, this will produce incorrect results: inverse then transpose should be used instead. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, MATRIX must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, MATRIX must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

#### Projection matrices

[procedure] (ortho WIDTH HEIGHT NEAR FAR [RESULT])

Create an orthographic projection matrix. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (ortho-viewport LEFT RIGHT NEAR FAR VIEWPORT-LEFT VIEWPORT-RIGHT VIEWPORT-BOTTOM VIEWPORT-TOP [RESULT])

Create an orthographic projection matrix mapping the LEFT, RIGHT, TOP, BOTTOM, NEAR, FAR cube to a viewport of VIEWPORT-LEFT, VIEWPORT-RIGHT, VIEWPORT-TOP, VIEWPORT-BOTTOM. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (perspective WIDTH HEIGHT NEAR FAR ANGLE [RESULT])

Create an perspective projection matrix with a field of view of ANGLE degrees. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (frustum LEFT RIGHT BOTTOM TOP NEAR FAR [RESULT])

Create a perspective projection matrix defined by a frustum with a near side of LEFT, RIGHT, TOP, BOTTOM, NEAR, and a far side at FAR. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (frustum-viewport LEFT RIGHT BOTTOM TOP NEAR FAR VIEWPORT-LEFT VIEWPORT-RIGHT VIEWPORT-BOTTOM VIEWPORT-TOP [RESULT])

Create a perspective projection matrix mapping the LEFT, RIGHT, TOP, BOTTOM, NEAR, FAR frustum to a viewport of VIEWPORT-LEFT, VIEWPORT-RIGHT, VIEWPORT-BOTTOM, VIEWPORT-TOP. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

#### Camera functions

[procedure] (look-at EYE OBJ UP [RESULT])

Create a “look-at” style camera matrix. The camera is positioned at point EYE, pointing towards the point OBJ. UP defines the camera’s up vector. If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (camera-inverse CAMERA [RESULT])

Invert CAMERA in an efficient fashion. This allows the camera to be constructed in an intuitive fashion by translating and rotating before inverting in order to position the scene properly. This function is far faster than the general inverse function, but the matrix CAMERA must only be a matrix representing a translation and a rotation (no scaling). If the matrix RESULT is given, it will be modified to contain the result. If RESULT is #t, CAMERA must be an f32vector and the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, CAMERA must be an f32vector and the returned value will be an f32vector located in normal garbage collected memory.

#### Vector operations

[procedure] (make-point X Y Z [NON-GC?])
[procedure] (point-x POINT)
[procedure] (point-y POINT)
[procedure] (point-z POINT)
[procedure] (point-x-set! POINT)
[procedure] (point-y-set! POINT)
[procedure] (point-z-set! POINT)

Vector constructor, getters, and setters. If NON-GC? is #t, the point is created in a non-garbage-collected area (the memory will still be freed when there are no more references to the vector).

[procedure] (v+ A B [RESULT])

Return the result of the addition of vectors A and B. If the vector RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (v- A B [RESULT])

Return the result of the subtraction of vector B from A. If the vector RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (v* V S [RESULT])

Return the result of the multiplication of vector A with scalar S. If the vector RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (cross-product A B [RESULT])

Return the result of the cross product between the vectors A and B. If the vector RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (dot-product A B)

Return the result of the dot product between the vectors A and B.

[procedure] (vector-magnitude V)

Return the magnitude of vector V.

[procedure] (normalize! V)

Destructively normalize the vector V.

[procedure] (m*vector! MATRIX VECTOR)

Destructively multiply VECTOR by MATRIX.

[procedure] (m*vector-array! MATRIX VECTORS stride: [STRIDE] length: [LENGTH])

Destructively multiply the array of 3 element floats VECTORS by MATRIX. VECTORS may be given as an f32vector, a u8vector or a pointer. The keyword STRIDE specifies the number of elements between consecutive vectors, given in number of floats (which must be at least 3) when VECTORS is an f32vector and in bytes when VECTORS is a u8vector or a pointer. When VECTORS is given as a pointer, the keyword LENGTH must be provided, specifying the number of vectors in VECTORS.

[procedure] (lerp A B T [RESULT])

Linear interpolation between the points A and B with the interpolation parameter T which must be between 0 and 1. If the vector RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

#### Quaternion operations

Quaternions are expected to be normalized before they are used in certain functions (quaternion-normalize! may be used to do so). All the provided functions that create quaternions, create unit quaternions.

The order of quaternion cross-multiplication is the inverse of the “standard” order, so a quaternion that has undergone a series or rotations will represent the same rotation as a marix that has gone through the same series, in the same order.

[procedure] (make-quaternion X Y Z W [NON-GC?])
[procedure] (quaternion-x POINT)
[procedure] (quaternion-y POINT)
[procedure] (quaternion-z POINT)
[procedure] (quaternion-w POINT)
[procedure] (quaternion-x-set! POINT)
[procedure] (quaternion-y-set! POINT)
[procedure] (quaternion-z-set! POINT)
[procedure] (quaternion-w-set! POINT)

Quaternion constructor, getters, and setters. If NON-GC is #t, the quaternion is created in a non-garbage-collected area (the memory will still be freed when there are no more references to the quaternion).

[procedure] (quaternion-normalize! Q)

Destructively normalize the quaternion Q.

[procedure] (quaternion-inverse Q [RESULT])

Return the inverse of the unit quaternion Q. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-cross-product A B [RESULT])

Return the cross-product of the quaternions A and B. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-axis-angle-rotation AXIS ANGLE [RESULT])

Return the quaternion corresponding to a rotation of ANGLE radians around the vector AXIS. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-rotate-axis-angle AXIS ANGLE Q)

Rotate the quaternion Q by a rotation of ANGLE radians around the vector AXIS.

[procedure] (quaternion-x-rotation ANGLE [RESULT])

Return the quaternion corresponding to a rotation of ANGLE radians around the x-axis. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-rotate-x ANGLE Q)

Rotate the quaternion Q by a rotation of ANGLE radians around the x-axis.

[procedure] (quaternion-y-rotation ANGLE [RESULT])

Return the quaternion corresponding to a rotation of ANGLE radians around the y-axis. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-rotate-y ANGLE Q)

Rotate the quaternion Q by a rotation of ANGLE radians around the y-axis.

[procedure] (quaternion-z-rotation ANGLE [RESULT])

Return the quaternion corresponding to a rotation of ANGLE radians around the z-axis. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-rotate-z ANGLE Q)

Rotate the quaternion Q by a rotation of ANGLE radians around the z-axis.

[procedure] (quaternion-ypr-rotation YAW PITCH ROLL [RESULT])

Return the quaternion corresponding to a rotation of ROLL radians around the z-axis followed by PITCH radians around the x-axis followed by YAW radians around the y-axis. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

[procedure] (quaternion-rotate-ypr YAW PITCH ROLL Q)

Rotate the quaternion Q by ROLL radians around the z-axis followed by PITCH radians around the x-axis followed by YAW radians around the y-axis.

[procedure] (quaternion-rotate-point! Q P)

Destructively rotate the point P by the unit quaternion Q.

[procedure] (slerp A B T [RESULT])

Spherical linear interpolation between the quaternions A and B with the interpolation parameter T which must be between 0 and 1. If the quaternion RESULT is given, it will be modified to contain the result. If RESULT is #t the returned value will be an f32vector located in non-garbage-collected memory (the memory will still be freed when there are no more references to the matrix). If RESULT is not provided, the returned value will be an f32vector located in normal garbage collected memory.

#### Angle operations

Converts ANGLE from degrees to radians.

Converts ANGLE from radians to degrees.

[constant] pi
[constant] pi/2

### Example

```
(import gl-math)

(define projection-matrix
(perspective 640 480 0.1 100 70))

(define view-matrix
(look-at (make-point 1 0 3)
(make-point 0 0 0)
(make-point 0 1 0)))

(define model-matrix (mat4-identity))

(print-mat4 (m* projection-matrix
(m* view-matrix model-matrix)))```

### Version history

#### Version 0.9.1

4 April 2019

• Fix a bug in make-quaternion
• point and quaternion constructors and setters now convert arguments to flonum automatically

#### Version 0.9.0

15 March 2019

• Maintenance given to Kooda
• Port to CHICKEN 5

7 August 2014

8 October 2014

#### Version 0.5.2

10 September 2014

• m*vector-array!: Stride is given in bytes when vector is a pointer

Version 0.5.0

2 September 2014

• Many new vector and quaternion functions
• Functions that previously accepted vectors as individual floats, now accept them as f32vectors

#### Version 0.4.1

30 August 2014

• Fix m*vector-array!

Version 0.4.0

27 July 2014

#### Version 0.3.2

21 July 2014

• Allow pointer to array of vectors to be passed to m*vector-array!
• Fix error forms

Version 0.3.1

23 June 2014

• Matrix vector multiplication

#### Version 0.2.0

21 June 2014

• Each transformation function now has two variants: one that initializes a matrix, and one that operates on a matrix
• Provide pi/2
• Provide quaternion and YPR rotation
• Fix optional arguments for matrix operations
• Fix a bug in look-at

#### Version 0.1.0

17 June 2014

• Initial release

### Source repository

Source available here.

Bug reports and patches welcome! Bugs can be reported to kooda@upyum.com

Alex Charlton