The mathkit Reference Manual

This is the mathkit Reference Manual, version 0.0, generated automatically by Declt version 4.0 beta 2 "William Riker" on Mon Aug 15 05:19:03 2022 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.

mathkit

2.1 `mathkit`

Various utilities for math

Author

License

MIT

Version

0.0

Dependencies

alexandria (system).
sb-cga (system).

Source

mathkit.asd.

Child 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.

Lisp

3.1.1 `mathkit/mathkit.asd`

Source: mathkit.asd.
Parent Component: mathkit (system).
ASDF Systems: mathkit.
Packages: mathkit.asdf.

3.1.2 `mathkit/package.lisp`

Source: mathkit.asd.
Parent Component: mathkit (system).
Packages: kit.math.

3.1.3 `mathkit/math.lisp`

Dependency

package.lisp (file).

Source

mathkit.asd.

Parent Component

mathkit (system).

Public Interface

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).

Internals

floatify (macro).
v (function).

3.1.4 `mathkit/quat.lisp`

Dependency

math.lisp (file).

Source

mathkit.asd.

Parent Component

mathkit (system).

Internals

%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).

Source

mathkit.asd.

Parent Component

mathkit (system).

Public Interface

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).

Internals

define-vecn (macro).

4 Packages

Packages are listed by definition order.

mathkit.asdf
kit.math

4.1 `mathkit.asdf`

Source

mathkit.asd.

Use List

asdf/interface.
common-lisp.

4.2 `kit.math`

Source

package.lisp.

Use List

common-lisp.
sb-cga.

Public Interface

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).

Internals

%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.

Public Interface
Internals

5.1 Public Interface

Ordinary functions
Types

5.1.1 Ordinary functions

Function: copy-matrix (m) ¶

Package: kit.math.
Source: math.lisp.

Function: deg-to-rad (x) ¶

Converts X, a number, from degrees to radians.

Package: kit.math.
Source: math.lisp.

Function: dvec2 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: dvec3 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: dvec4 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

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.

Function: ivec2 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: ivec3 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: ivec4 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

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.

Function: matrix*vec3 (vec matrix) ¶

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

Package: kit.math.
Alias for: transform-point.

Function: matrix*vec4 (matrix vector) ¶

Package: kit.math.
Source: math.lisp.

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.

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.

Function: rad-to-deg (x) ¶

Converts X, a number, from radians to degrees.

Package: kit.math.
Source: math.lisp.

Function: unproject (point model-matrix perspective-matrix viewport) ¶

Package: kit.math.
Source: math.lisp.

Function: vec2 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: vec3 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

Function: vec4 (a &rest r) ¶

Package: kit.math.
Source: vector.lisp.

5.1.2 Types

Type: dvec2 () ¶

Package: kit.math.
Source: vector.lisp.

Type: dvec3 () ¶

Package: kit.math.
Source: vector.lisp.

Type: dvec4 () ¶

Package: kit.math.
Source: vector.lisp.

Type: ivec2 () ¶

Package: kit.math.
Source: vector.lisp.

Type: ivec3 () ¶

Package: kit.math.
Source: vector.lisp.

Type: ivec4 () ¶

Package: kit.math.
Source: vector.lisp.

Type: vec2 () ¶

Package: kit.math.
Source: vector.lisp.

Type: vec3 () ¶

Package: kit.math.
Source: vector.lisp.

Type: vec4 () ¶

Package: kit.math.
Source: vector.lisp.

5.2 Internals

Macros
Ordinary functions
Types

5.2.1 Macros

Macro: define-vecn (n type &optional prefix) ¶

Package: kit.math.
Source: vector.lisp.

Macro: defun-qrot (nname name index &optional post) ¶

Package: kit.math.
Source: quat.lisp.

Macro: floatify ((&rest symbols) &body body) ¶

Package: kit.math.
Source: math.lisp.

5.2.2 Ordinary 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.

Function: %quat* (a b dest) ¶

multiply quaternions A and B storing result into DEST.

Package: kit.math.
Source: quat.lisp.

Function: angle-axis->dquaternion (angle-radians axis) ¶

create a quaternion from specified axis and angle in radians

Package: kit.math.
Source: quat.lisp.

Function: angle-axis->quaternion (angle-radians axis) ¶

create a quaternion from specified axis and angle in radians

Package: kit.math.
Source: quat.lisp.

Function: copy-quaternion (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: dquat* (a b &rest rest) ¶

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

Package: kit.math.
Source: quat.lisp.

Function: dquaternion (w x y z) ¶

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

Package: kit.math.
Source: quat.lisp.

Function: nqlerp (a b f) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-local-x (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-local-y (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-local-z (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-world-x (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-world-y (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-nrotate-world-z (quat angle dest) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-local-x (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-local-y (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-local-z (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-world-x (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-world-y (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: q-rotate-world-z (quat angle) ¶

Package: kit.math.
Source: quat.lisp.

Function: qi (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: qj (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: qk (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: quat* (a b &rest rest) ¶

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

Package: kit.math.
Source: quat.lisp.

Function: quat+ (a b) ¶

Package: kit.math.
Source: quat.lisp.

Function: quat- (a b) ¶

Package: kit.math.
Source: quat.lisp.

Function: quat->axis-angle (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: quat-inverse (quat) ¶

Package: kit.math.
Source: quat.lisp.

Function: quat-rotate-matrix (quat &optional matrix) ¶

Package: kit.math.
Source: quat.lisp.

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.

Function: quaternion (w x y z) ¶

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

Package: kit.math.
Source: quat.lisp.

Function: qw (q) ¶

Package: kit.math.
Source: quat.lisp.

Function: v (l) ¶

Package: kit.math.
Source: math.lisp.

Function: vx (v) ¶

Package: kit.math.
Source: quat.lisp.

Function: vy (v) ¶

Package: kit.math.
Source: quat.lisp.

Function: vz (v) ¶

Package: kit.math.
Source: quat.lisp.

5.2.3 Types

Type: dquaternion () ¶

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

Package: kit.math.
Source: quat.lisp.

Type: quaternion () ¶

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

Package: kit.math.
Source: quat.lisp.

Appendix A Indexes

Concepts
Functions
Variables
Data types

A.1 Concepts

A.2 Functions

Jump to:	% A C D F I L M N O P Q R U V

	Index Entry	Section

%
	`%nq*`:	Private ordinary functions
	`%quat*`:	Private ordinary functions

A
	`angle-axis->dquaternion`:	Private ordinary functions
	`angle-axis->quaternion`:	Private ordinary functions

C
	`copy-matrix`:	Public ordinary functions
	`copy-quaternion`:	Private ordinary functions

D
	`define-vecn`:	Private macros
	`defun-qrot`:	Private macros
	`deg-to-rad`:	Public ordinary functions
	`dquat*`:	Private ordinary functions
	`dquaternion`:	Private ordinary functions
	`dvec2`:	Public ordinary functions
	`dvec3`:	Public ordinary functions
	`dvec4`:	Public ordinary functions

F
	`floatify`:	Private macros
	`frustum`:	Public ordinary functions
	`Function, %nq*`:	Private ordinary functions
	`Function, %quat*`:	Private ordinary functions
	`Function, angle-axis->dquaternion`:	Private ordinary functions
	`Function, angle-axis->quaternion`:	Private ordinary functions
	`Function, copy-matrix`:	Public ordinary functions
	`Function, copy-quaternion`:	Private ordinary functions
	`Function, deg-to-rad`:	Public ordinary functions
	`Function, dquat*`:	Private ordinary functions
	`Function, dquaternion`:	Private ordinary functions
	`Function, dvec2`:	Public ordinary functions
	`Function, dvec3`:	Public ordinary functions
	`Function, dvec4`:	Public ordinary functions
	`Function, frustum`:	Public ordinary functions
	`Function, ivec2`:	Public ordinary functions
	`Function, ivec3`:	Public ordinary functions
	`Function, ivec4`:	Public ordinary functions
	`Function, look-at`:	Public ordinary functions
	`Function, matrix*vec3`:	Public ordinary functions
	`Function, matrix*vec4`:	Public ordinary functions
	`Function, nqlerp`:	Private ordinary functions
	`Function, ortho-matrix`:	Public ordinary functions
	`Function, perspective-matrix`:	Public ordinary functions
	`Function, q-nrotate-local-x`:	Private ordinary functions
	`Function, q-nrotate-local-y`:	Private ordinary functions
	`Function, q-nrotate-local-z`:	Private ordinary functions
	`Function, q-nrotate-world-x`:	Private ordinary functions
	`Function, q-nrotate-world-y`:	Private ordinary functions
	`Function, q-nrotate-world-z`:	Private ordinary functions
	`Function, q-rotate-local-x`:	Private ordinary functions
	`Function, q-rotate-local-y`:	Private ordinary functions
	`Function, q-rotate-local-z`:	Private ordinary functions
	`Function, q-rotate-world-x`:	Private ordinary functions
	`Function, q-rotate-world-y`:	Private ordinary functions
	`Function, q-rotate-world-z`:	Private ordinary functions
	`Function, qi`:	Private ordinary functions
	`Function, qj`:	Private ordinary functions
	`Function, qk`:	Private ordinary functions
	`Function, quat*`:	Private ordinary functions
	`Function, quat+`:	Private ordinary functions
	`Function, quat-`:	Private ordinary functions
	`Function, quat->axis-angle`:	Private ordinary functions
	`Function, quat-inverse`:	Private ordinary functions
	`Function, quat-rotate-matrix`:	Private ordinary functions
	`Function, quat-rotate-vector`:	Private ordinary functions
	`Function, quaternion`:	Private ordinary functions
	`Function, qw`:	Private ordinary functions
	`Function, rad-to-deg`:	Public ordinary functions
	`Function, unproject`:	Public ordinary functions
	`Function, v`:	Private ordinary functions
	`Function, vec2`:	Public ordinary functions
	`Function, vec3`:	Public ordinary functions
	`Function, vec4`:	Public ordinary functions
	`Function, vx`:	Private ordinary functions
	`Function, vy`:	Private ordinary functions
	`Function, vz`:	Private ordinary functions

I
	`ivec2`:	Public ordinary functions
	`ivec3`:	Public ordinary functions
	`ivec4`:	Public ordinary functions

L
	`look-at`:	Public ordinary functions

M
	`Macro, define-vecn`:	Private macros
	`Macro, defun-qrot`:	Private macros
	`Macro, floatify`:	Private macros
	`matrix*vec3`:	Public ordinary functions
	`matrix*vec4`:	Public ordinary functions

N
	`nqlerp`:	Private ordinary functions

O
	`ortho-matrix`:	Public ordinary functions

P
	`perspective-matrix`:	Public ordinary functions

Q
	`q-nrotate-local-x`:	Private ordinary functions
	`q-nrotate-local-y`:	Private ordinary functions
	`q-nrotate-local-z`:	Private ordinary functions
	`q-nrotate-world-x`:	Private ordinary functions
	`q-nrotate-world-y`:	Private ordinary functions
	`q-nrotate-world-z`:	Private ordinary functions
	`q-rotate-local-x`:	Private ordinary functions
	`q-rotate-local-y`:	Private ordinary functions
	`q-rotate-local-z`:	Private ordinary functions
	`q-rotate-world-x`:	Private ordinary functions
	`q-rotate-world-y`:	Private ordinary functions
	`q-rotate-world-z`:	Private ordinary functions
	`qi`:	Private ordinary functions
	`qj`:	Private ordinary functions
	`qk`:	Private ordinary functions
	`quat*`:	Private ordinary functions
	`quat+`:	Private ordinary functions
	`quat-`:	Private ordinary functions
	`quat->axis-angle`:	Private ordinary functions
	`quat-inverse`:	Private ordinary functions
	`quat-rotate-matrix`:	Private ordinary functions
	`quat-rotate-vector`:	Private ordinary functions
	`quaternion`:	Private ordinary functions
	`qw`:	Private ordinary functions

R
	`rad-to-deg`:	Public ordinary functions

U
	`unproject`:	Public ordinary functions

V
	`v`:	Private ordinary functions
	`vec2`:	Public ordinary functions
	`vec3`:	Public ordinary functions
	`vec4`:	Public ordinary functions
	`vx`:	Private ordinary functions
	`vy`:	Private ordinary functions
	`vz`:	Private ordinary functions

Jump to:	% A C D F I L M N O P Q R U V

A.3 Variables

A.4 Data types

Jump to:	D F I K M P Q S T V

	Index Entry	Section

D
	`dquaternion`:	Private types
	`dvec2`:	Public types
	`dvec3`:	Public types
	`dvec4`:	Public types

F
	`File, math.lisp`:	The mathkit/math․lisp file
	`File, mathkit.asd`:	The mathkit/mathkit․asd file
	`File, package.lisp`:	The mathkit/package․lisp file
	`File, quat.lisp`:	The mathkit/quat․lisp file
	`File, vector.lisp`:	The mathkit/vector․lisp file

I
	`ivec2`:	Public types
	`ivec3`:	Public types
	`ivec4`:	Public types

K
	`kit.math`:	The kit․math package

M
	`math.lisp`:	The mathkit/math․lisp file
	`mathkit`:	The mathkit system
	`mathkit.asd`:	The mathkit/mathkit․asd file
	`mathkit.asdf`:	The mathkit․asdf package

P
	`Package, kit.math`:	The kit․math package
	`Package, mathkit.asdf`:	The mathkit․asdf package
	`package.lisp`:	The mathkit/package․lisp file

Q
	`quat.lisp`:	The mathkit/quat․lisp file
	`quaternion`:	Private types

S
	`System, mathkit`:	The mathkit system

T
	`Type, dquaternion`:	Private types
	`Type, dvec2`:	Public types
	`Type, dvec3`:	Public types
	`Type, dvec4`:	Public types
	`Type, ivec2`:	Public types
	`Type, ivec3`:	Public types
	`Type, ivec4`:	Public types
	`Type, quaternion`:	Private types
	`Type, vec2`:	Public types
	`Type, vec3`:	Public types
	`Type, vec4`:	Public types

V
	`vec2`:	Public types
	`vec3`:	Public types
	`vec4`:	Public types
	`vector.lisp`:	The mathkit/vector․lisp file

Jump to:	D F I K M P Q S T V

The mathkit Reference Manual

The mathkit Reference Manual

Table of Contents

1 Introduction

mathkit

2 Systems

2.1 mathkit

3 Files

3.1 Lisp

3.1.1 mathkit/mathkit.asd

3.1.2 mathkit/package.lisp

3.1.3 mathkit/math.lisp

3.1.4 mathkit/quat.lisp

3.1.5 mathkit/vector.lisp

4 Packages

4.1 mathkit.asdf

4.2 kit.math

5 Definitions

5.1 Public Interface

5.1.1 Ordinary functions

5.1.2 Types

5.2 Internals

5.2.1 Macros

5.2.2 Ordinary functions

5.2.3 Types

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types

2.1 `mathkit`

3.1.1 `mathkit/mathkit.asd`

3.1.2 `mathkit/package.lisp`

3.1.3 `mathkit/math.lisp`

3.1.4 `mathkit/quat.lisp`

3.1.5 `mathkit/vector.lisp`

4.1 `mathkit.asdf`

4.2 `kit.math`