The mathkit Reference Manual

Table of Contents

The mathkit Reference Manual

This is the mathkit Reference Manual, version 0.0, generated automatically by Declt version 3.0 "Montgomery Scott" on Fri Jun 26 11:43:19 2020 GMT+0.

1 Introduction

mathkit

This is a purely math-related utility kit, providing functions which can be useful for games, 3D, and GL in general. Right now this includes additional matrix functionality by @3b on top of sb-cga.

• ortho-matrix LEFT RIGHT BOTTOM TOP NEAR FAR: Construct an orthographic matrix like glOrtho from OpenGL 2.1.
• frustum LEFT RIGHT BOTTOM TOP NEAR FAR: Construct a perspective matrix from the given parameters, like glFrustum from OpenGL 2.1.
• perspective-matrix FOVY-DEGREES ASPECT Z-NEAR Z-FAR: Construct a perspective matrix from the given parameters, like gluPerspective from OpenGL 2.1.
• look-at EYE TARGET UP: Where EYE, TARGET, and UP are vectors, construct a viewing matrix much like gluLookAt from OpenGL 2.1.

Note: These merely create native Lisp matrices; they do not multiply them like the similar GL functions or in any way set them as GL state like the old fixed-function pipeline.

Additionally:

• copy-matrix M: Create a copy of M.
• deg-to-rad D: Convert D degrees to radians.

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 mathkit

Author

3b

License

MIT

Description

Various utilities for math

Version

0.0

Dependencies

• alexandria
• sb-cga

Source

mathkit.asd (file)

Components

• package.lisp (file)
• math.lisp (file)
• quat.lisp (file)
• vector.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 mathkit.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/mathkit-20160208-git/mathkit.asd

Systems

mathkit (system)

Packages

mathkit.asdf

3.1.2 mathkit/package.lisp

Parent

mathkit (system)

Location

package.lisp

Packages

kit.math

3.1.3 mathkit/math.lisp

Dependency

package.lisp (file)

Parent

mathkit (system)

Location

math.lisp

Exported Definitions

• copy-matrix (function)
• deg-to-rad (function)
• frustum (function)
• look-at (function)
• matrix*vec4 (function)
• ortho-matrix (function)
• perspective-matrix (function)
• rad-to-deg (function)
• unproject (function)

Internal Definitions

• floatify (macro)
• v (function)

3.1.4 mathkit/quat.lisp

Dependency

math.lisp (file)

Parent

mathkit (system)

Location

quat.lisp

Internal Definitions

• %nq* (function)
• %quat* (function)
• angle-axis->dquaternion (function)
• angle-axis->quaternion (function)
• copy-quaternion (function)
• defun-qrot (macro)
• dquat* (function)
• dquaternion (function)
• dquaternion (type)
• nqlerp (function)
• q-nrotate-local-x (function)
• q-nrotate-local-y (function)
• q-nrotate-local-z (function)
• q-nrotate-world-x (function)
• q-nrotate-world-y (function)
• q-nrotate-world-z (function)
• q-rotate-local-x (function)
• q-rotate-local-y (function)
• q-rotate-local-z (function)
• q-rotate-world-x (function)
• q-rotate-world-y (function)
• q-rotate-world-z (function)
• qi (function)
• qj (function)
• qk (function)
• quat* (function)
• quat+ (function)
• quat- (function)
• quat->axis-angle (function)
• quat-inverse (function)
• quat-rotate-matrix (function)
• quat-rotate-vector (function)
• quaternion (function)
• quaternion (type)
• qw (function)
• vx (function)
• vy (function)
• vz (function)

3.1.5 mathkit/vector.lisp

Dependency

quat.lisp (file)

Parent

mathkit (system)

Location

vector.lisp

Exported Definitions

• dvec2 (function)
• dvec2 (type)
• dvec3 (function)
• dvec3 (type)
• dvec4 (function)
• dvec4 (type)
• ivec2 (function)
• ivec2 (type)
• ivec3 (function)
• ivec3 (type)
• ivec4 (function)
• ivec4 (type)
• vec2 (function)
• vec2 (type)
• vec3 (function)
• vec3 (type)
• vec4 (function)
• vec4 (type)

Internal Definitions

define-vecn (macro)

4 Packages

Packages are listed by definition order.

4.1 mathkit.asdf

Source

/home/quickref/quicklisp/dists/quicklisp/software/mathkit-20160208-git/mathkit.asd

Use List

• asdf/interface
• common-lisp

4.2 kit.math

Source

package.lisp (file)

Use List

• sb-cga
• common-lisp

Exported Definitions

• copy-matrix (function)
• deg-to-rad (function)
• dvec2 (function)
• dvec2 (type)
• dvec3 (function)
• dvec3 (type)
• dvec4 (function)
• dvec4 (type)
• frustum (function)
• ivec2 (function)
• ivec2 (type)
• ivec3 (function)
• ivec3 (type)
• ivec4 (function)
• ivec4 (type)
• look-at (function)
• matrix*vec3 (function)
• matrix*vec4 (function)
• ortho-matrix (function)
• perspective-matrix (function)
• rad-to-deg (function)
• unproject (function)
• vec2 (function)
• vec2 (type)
• vec3 (function)
• vec3 (type)
• vec4 (function)
• vec4 (type)

Internal Definitions

• %nq* (function)
• %quat* (function)
• angle-axis->dquaternion (function)
• angle-axis->quaternion (function)
• copy-quaternion (function)
• define-vecn (macro)
• defun-qrot (macro)
• dquat* (function)
• dquaternion (function)
• dquaternion (type)
• floatify (macro)
• nqlerp (function)
• q-nrotate-local-x (function)
• q-nrotate-local-y (function)
• q-nrotate-local-z (function)
• q-nrotate-world-x (function)
• q-nrotate-world-y (function)
• q-nrotate-world-z (function)
• q-rotate-local-x (function)
• q-rotate-local-y (function)
• q-rotate-local-z (function)
• q-rotate-world-x (function)
• q-rotate-world-y (function)
• q-rotate-world-z (function)
• qi (function)
• qj (function)
• qk (function)
• quat* (function)
• quat+ (function)
• quat- (function)
• quat->axis-angle (function)
• quat-inverse (function)
• quat-rotate-matrix (function)
• quat-rotate-vector (function)
• quaternion (function)
• quaternion (type)
• qw (function)
• v (function)
• vx (function)
• vy (function)
• vz (function)

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Functions

Function: copy-matrix M

Package

kit.math

Source

math.lisp (file)

Function: deg-to-rad X

Converts X, a number, from degrees to radians.

Package

kit.math

Source

math.lisp (file)

Function: dvec2 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: dvec3 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: dvec4 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: frustum LEFT RIGHT BOTTOM TOP NEAR FAR

Returns a projection matrix that is similar to the glFrustum matrix.

LEFT, RIGHT, BOTTOM, TOP, NEAR and FAR are numbers representing their respective clipping planes. NEAR and FAR must be positive.

Package

kit.math

Source

math.lisp (file)

Function: ivec2 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: ivec3 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: ivec4 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: look-at EYE TARGET UP

Returns a view matrix that is similar to the gluLookAt matrix.

EYE and TARGET are both three dimensional coordinate vectors, with the former representing the eye’s location and the latter the center of its viewing target.

UP is a direction vector, representing which way is up for the eye.

Package

kit.math

Source

math.lisp (file)

Function: matrix*vec3 VEC MATRIX

Apply transformation MATRIX to VEC, return result as a freshly allocated VEC.

Package

kit.math

Source

/home/quickref/quicklisp/dists/quicklisp/software/sb-cga-20171227-git/vec.lisp

Function: matrix*vec4 MATRIX VECTOR

Package

kit.math

Source

math.lisp (file)

Function: ortho-matrix LEFT RIGHT BOTTOM TOP NEAR FAR

Returns a projection matrix that is similar to the glOrtho matrix.

LEFT, RIGHT, BOTTOM, TOP, NEAR and FAR are numbers representing their respective clipping planes.

Package

kit.math

Source

math.lisp (file)

Function: perspective-matrix FOVY ASPECT Z-NEAR Z-FAR

Returns a projection matrix that is similar to the gluPerspective matrix.

FOVY is the field of view, in degrees.

ASPECT is the aspect ratio of the window, width / height.

Z-NEAR and Z-FAR are positive numbers representing the depth clipping planes.

Package

kit.math

Source

math.lisp (file)

Function: rad-to-deg X

Converts X, a number, from radians to degrees.

Package

kit.math

Source

math.lisp (file)

Function: unproject POINT MODEL-MATRIX PERSPECTIVE-MATRIX VIEWPORT

Package

kit.math

Source

math.lisp (file)

Function: vec2 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: vec3 A &rest R

Package

kit.math

Source

vector.lisp (file)

Function: vec4 A &rest R

Package

kit.math

Source

vector.lisp (file)

5.1.2 Types

Type: dvec2 ()

Package

kit.math

Source

vector.lisp (file)

Type: dvec3 ()

Package

kit.math

Source

vector.lisp (file)

Type: dvec4 ()

Package

kit.math

Source

vector.lisp (file)

Type: ivec2 ()

Package

kit.math

Source

vector.lisp (file)

Type: ivec3 ()

Package

kit.math

Source

vector.lisp (file)

Type: ivec4 ()

Package

kit.math

Source

vector.lisp (file)

Type: vec2 ()

Package

kit.math

Source

vector.lisp (file)

Type: vec3 ()

Package

kit.math

Source

vector.lisp (file)

Type: vec4 ()

Package

kit.math

Source

vector.lisp (file)

5.2 Internal definitions

5.2.1 Macros

Macro: define-vecn N TYPE &optional PREFIX

Package

kit.math

Source

vector.lisp (file)

Macro: defun-qrot NNAME NAME INDEX &optional POST

Package

kit.math

Source

quat.lisp (file)

Macro: floatify (&rest SYMBOLS) &body BODY

Package

kit.math

Source

math.lisp (file)

5.2.2 Functions

Function: %nq* A1 A2 A3 A4 B1 B2 B3 B4

multiply 2 quaternions with elements A{1..4} and B{1..4}, returning result as multiple values.

Package

kit.math

Source

quat.lisp (file)

Function: %quat* A B DEST

multiply quaternions A and B storing result into DEST.

Package

kit.math

Source

quat.lisp (file)

Function: angle-axis->dquaternion ANGLE-RADIANS AXIS

create a quaternion from specified axis and angle in radians

Package

kit.math

Source

quat.lisp (file)

Function: angle-axis->quaternion ANGLE-RADIANS AXIS

create a quaternion from specified axis and angle in radians

Package

kit.math

Source

quat.lisp (file)

Function: copy-quaternion Q

Package

kit.math

Source

quat.lisp (file)

Function: dquat* A B &rest REST

multiply quaternions A and B returning result as a new quaternion.

Package

kit.math

Source

quat.lisp (file)

Function: dquaternion W X Y Z

Allocate dquaternion [W, Xi, Yj, Zk].

Package

kit.math

Source

quat.lisp (file)

Function: nqlerp A B F

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-local-x QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-local-y QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-local-z QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-world-x QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-world-y QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-nrotate-world-z QUAT ANGLE DEST

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-local-x QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-local-y QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-local-z QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-world-x QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-world-y QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: q-rotate-world-z QUAT ANGLE

Package

kit.math

Source

quat.lisp (file)

Function: qi Q

Package

kit.math

Source

quat.lisp (file)

Function: qj Q

Package

kit.math

Source

quat.lisp (file)

Function: qk Q

Package

kit.math

Source

quat.lisp (file)

Function: quat* A B &rest REST

multiply quaternions A and B returning result as a new quaternion.

Package

kit.math

Source

quat.lisp (file)

Function: quat+ A B

Package

kit.math

Source

quat.lisp (file)

Function: quat- A B

Package

kit.math

Source

quat.lisp (file)

Function: quat->axis-angle Q

Package

kit.math

Source

quat.lisp (file)

Function: quat-inverse QUAT

Package

kit.math

Source

quat.lisp (file)

Function: quat-rotate-matrix QUAT &optional MATRIX

Package

kit.math

Source

quat.lisp (file)

Function: quat-rotate-vector QUAT VEC

rotate a vector VEC using specifed rotation quaternion Q, returning result as a new single-float vector.

Package

kit.math

Source

quat.lisp (file)

Function: quaternion W X Y Z

Allocate quaternion [W, Xi, Yj, Zk].

Package

kit.math

Source

quat.lisp (file)

Function: qw Q

Package

kit.math

Source

quat.lisp (file)

Function: v L

Package

kit.math

Source

math.lisp (file)

Function: vx V

Package

kit.math

Source

quat.lisp (file)

Function: vy V

Package

kit.math

Source

quat.lisp (file)

Function: vz V

Package

kit.math

Source

quat.lisp (file)

5.2.3 Types

Type: dquaternion ()

A quaternion of double floats. [W, Xi, Yj, Zk]

Package

kit.math

Source

quat.lisp (file)

Type: quaternion ()

A quaternion of single floats. [W, Xi, Yj, Zk]

Package

kit.math

Source

quat.lisp (file)

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types