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;;; Chickadee Game Toolkit
;;; Copyright © 2016 David Thompson <davet@gnu.org>
;;;
;;; Chickadee is free software: you can redistribute it and/or modify
;;; it under the terms of the GNU General Public License as published
;;; by the Free Software Foundation, either version 3 of the License,
;;; or (at your option) any later version.
;;;
;;; Chickadee is distributed in the hope that it will be useful, but
;;; WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program. If not, see
;;; <http://www.gnu.org/licenses/>.
(define-module (chickadee math matrix)
#:use-module (ice-9 match)
#:use-module (rnrs bytevectors)
#:use-module (srfi srfi-9)
#:use-module (srfi srfi-9 gnu)
#:use-module (srfi srfi-4)
#:use-module (system foreign)
#:use-module (chickadee math vector)
#:export (make-matrix4
make-null-matrix4
matrix4?
matrix4-mult!
matrix4*
matrix4-identity!
make-identity-matrix4
orthographic-projection
matrix4-translate!
matrix4-translate
matrix4-scale!
matrix4-scale
matrix4-rotate-z!
matrix4-rotate-z
transform))
;; 4x4 matrix
(define-record-type <matrix4>
(%make-matrix4 bv ptr)
matrix4?
(bv matrix4-bv)
(ptr matrix4-ptr))
(define-inlinable (matrix-set! matrix row column x)
(f32vector-set! matrix (+ (* row 4) column) x))
(define-inlinable (matrix-ref matrix row column)
(f32vector-ref matrix (+ (* row 4) column)))
(define (init-matrix4 matrix
aa ab ac ad
ba bb bc bd
ca cb cc cd
da db dc dd)
(let ((bv (matrix4-bv matrix)))
(matrix-set! bv 0 0 aa)
(matrix-set! bv 0 1 ab)
(matrix-set! bv 0 2 ac)
(matrix-set! bv 0 3 ad)
(matrix-set! bv 1 0 ba)
(matrix-set! bv 1 1 bb)
(matrix-set! bv 1 2 bc)
(matrix-set! bv 1 3 bd)
(matrix-set! bv 2 0 ca)
(matrix-set! bv 2 1 cb)
(matrix-set! bv 2 2 cc)
(matrix-set! bv 2 3 cd)
(matrix-set! bv 3 0 da)
(matrix-set! bv 3 1 db)
(matrix-set! bv 3 2 dc)
(matrix-set! bv 3 3 dd)))
(define (make-null-matrix4)
(let ((bv (make-f32vector 16)))
(%make-matrix4 bv (bytevector->pointer bv))))
(define (make-matrix4 aa ab ac ad
ba bb bc bd
ca cb cc cd
da db dc dd)
"Return a new 4x4 matrix initialized with the given 16 values in
column-major format."
(let ((matrix (make-null-matrix4)))
(init-matrix4 matrix
aa ab ac ad
ba bb bc bd
ca cb cc cd
da db dc dd)
matrix))
(define (matrix4-mult! dest a b)
"Multiply matrices A and B, storing the result in DEST."
(let ((m1 (matrix4-bv a))
(m2 (matrix4-bv b))
(m3 (matrix4-bv dest)))
(let ((m1-0-0 (matrix-ref m1 0 0))
(m1-0-1 (matrix-ref m1 0 1))
(m1-0-2 (matrix-ref m1 0 2))
(m1-0-3 (matrix-ref m1 0 3))
(m1-1-0 (matrix-ref m1 1 0))
(m1-1-1 (matrix-ref m1 1 1))
(m1-1-2 (matrix-ref m1 1 2))
(m1-1-3 (matrix-ref m1 1 3))
(m1-2-0 (matrix-ref m1 2 0))
(m1-2-1 (matrix-ref m1 2 1))
(m1-2-2 (matrix-ref m1 2 2))
(m1-2-3 (matrix-ref m1 2 3))
(m1-3-0 (matrix-ref m1 3 0))
(m1-3-1 (matrix-ref m1 3 1))
(m1-3-2 (matrix-ref m1 3 2))
(m1-3-3 (matrix-ref m1 3 3))
(m2-0-0 (matrix-ref m2 0 0))
(m2-0-1 (matrix-ref m2 0 1))
(m2-0-2 (matrix-ref m2 0 2))
(m2-0-3 (matrix-ref m2 0 3))
(m2-1-0 (matrix-ref m2 1 0))
(m2-1-1 (matrix-ref m2 1 1))
(m2-1-2 (matrix-ref m2 1 2))
(m2-1-3 (matrix-ref m2 1 3))
(m2-2-0 (matrix-ref m2 2 0))
(m2-2-1 (matrix-ref m2 2 1))
(m2-2-2 (matrix-ref m2 2 2))
(m2-2-3 (matrix-ref m2 2 3))
(m2-3-0 (matrix-ref m2 3 0))
(m2-3-1 (matrix-ref m2 3 1))
(m2-3-2 (matrix-ref m2 3 2))
(m2-3-3 (matrix-ref m2 3 3)))
(matrix-set! m3 0 0
(+ (* m1-0-0 m2-0-0)
(* m1-0-1 m2-1-0)
(* m1-0-2 m2-2-0)
(* m1-0-3 m2-3-0)))
(matrix-set! m3 0 1
(+ (* m1-0-0 m2-0-1)
(* m1-0-1 m2-1-1)
(* m1-0-2 m2-2-1)
(* m1-0-3 m2-3-1)))
(matrix-set! m3 0 2
(+ (* m1-0-0 m2-0-2)
(* m1-0-1 m2-1-2)
(* m1-0-2 m2-2-2)
(* m1-0-3 m2-3-2)))
(matrix-set! m3 0 3
(+ (* m1-0-0 m2-0-3)
(* m1-0-1 m2-1-3)
(* m1-0-2 m2-2-3)
(* m1-0-3 m2-3-3)))
(matrix-set! m3 1 0
(+ (* m1-1-0 m2-0-0)
(* m1-1-1 m2-1-0)
(* m1-1-2 m2-2-0)
(* m1-1-3 m2-3-0)))
(matrix-set! m3 1 1
(+ (* m1-1-0 m2-0-1)
(* m1-1-1 m2-1-1)
(* m1-1-2 m2-2-1)
(* m1-1-3 m2-3-1)))
(matrix-set! m3 1 2
(+ (* m1-1-0 m2-0-2)
(* m1-1-1 m2-1-2)
(* m1-1-2 m2-2-2)
(* m1-1-3 m2-3-2)))
(matrix-set! m3 1 3
(+ (* m1-1-0 m2-0-3)
(* m1-1-1 m2-1-3)
(* m1-1-2 m2-2-3)
(* m1-1-3 m2-3-3)))
(matrix-set! m3 2 0
(+ (* m1-2-0 m2-0-0)
(* m1-2-1 m2-1-0)
(* m1-2-2 m2-2-0)
(* m1-2-3 m2-3-0)))
(matrix-set! m3 2 1
(+ (* m1-2-0 m2-0-1)
(* m1-2-1 m2-1-1)
(* m1-2-2 m2-2-1)
(* m1-2-3 m2-3-1)))
(matrix-set! m3 2 2
(+ (* m1-2-0 m2-0-2)
(* m1-2-1 m2-1-2)
(* m1-2-2 m2-2-2)
(* m1-2-3 m2-3-2)))
(matrix-set! m3 2 3
(+ (* m1-2-0 m2-0-3)
(* m1-2-1 m2-1-3)
(* m1-2-2 m2-2-3)
(* m1-2-3 m2-3-3)))
(matrix-set! m3 3 0
(+ (* m1-3-0 m2-0-0)
(* m1-3-1 m2-1-0)
(* m1-3-2 m2-2-0)
(* m1-3-3 m2-3-0)))
(matrix-set! m3 3 1
(+ (* m1-3-0 m2-0-1)
(* m1-3-1 m2-1-1)
(* m1-3-2 m2-2-1)
(* m1-3-3 m2-3-1)))
(matrix-set! m3 3 2
(+ (* m1-3-0 m2-0-2)
(* m1-3-1 m2-1-2)
(* m1-3-2 m2-2-2)
(* m1-3-3 m2-3-2)))
(matrix-set! m3 3 3
(+ (* m1-3-0 m2-0-3)
(* m1-3-1 m2-1-3)
(* m1-3-2 m2-2-3)
(* m1-3-3 m2-3-3))))))
(define (matrix4-copy matrix)
(let ((bv (bytevector-copy (matrix4-bv matrix))))
(%make-matrix4 bv (bytevector->pointer bv))))
(define (matrix4* . matrices)
"Return the product of MATRICES."
(match matrices
(() (make-identity-matrix4))
((a b)
(let ((result (make-identity-matrix4)))
(matrix4-mult! result a b)
result))
((first . rest)
(let loop ((temp (make-identity-matrix4))
(prev (matrix4-copy first))
(matrices rest))
(match matrices
(() prev)
((current . rest)
(matrix4-mult! temp prev current)
(loop prev temp rest)))))))
(define (matrix4-identity! matrix)
(init-matrix4 matrix
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0 0.0 1.0))
(define (make-identity-matrix4)
(let ((matrix (make-null-matrix4)))
(matrix4-identity! matrix)
matrix))
(define (orthographic-projection left right top bottom near far)
"Return a new transform that represents an orthographic projection
for the vertical clipping plane LEFT and RIGHT, the horizontal
clipping plane TOP and BOTTOM, and the depth clipping plane NEAR and
FAR."
(make-matrix4 (/ 2 (- right left)) 0 0 0
0 (/ 2 (- top bottom)) 0 0
0 0 (/ 2 (- far near)) 0
(- (/ (+ right left) (- right left)))
(- (/ (+ top bottom) (- top bottom)))
(- (/ (+ far near) (- far near)))
1))
(define (matrix4-translate! matrix v)
(cond
((vector2? v)
(init-matrix4 matrix
1 0 0 0
0 1 0 0
0 0 1 0
(vx v) (vy v) 0 1))
((vector3? v)
(init-matrix4 matrix
1 0 0 0
0 1 0 0
0 0 1 0
(vx v) (vy v) (vz v) 1))
(else
(error "invalid translation vector" v))))
(define (matrix4-translate v)
(let ((matrix (make-null-matrix4)))
(matrix4-translate! matrix v)
matrix))
(define (matrix4-scale! matrix s)
(init-matrix4 matrix
s 0.0 0.0 0.0
0.0 s 0.0 0.0
0.0 0.0 s 0.0
0.0 0.0 0.0 1.0))
(define (matrix4-scale s)
(let ((matrix (make-null-matrix4)))
(matrix4-scale! matrix s)
matrix))
(define (matrix4-rotate-z! matrix angle)
(init-matrix4 matrix
(cos angle) (- (sin angle)) 0.0 0.0
(sin angle) (cos angle) 0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0 0.0 1.0))
(define (matrix4-rotate-z angle)
"Return a new matrix that rotates the Z axis by ANGLE radians."
(let ((matrix (make-null-matrix4)))
(matrix4-rotate-z! matrix angle)
matrix))
(define (transform matrix x y)
(let ((bv (matrix4-bv matrix)))
(values (+ (* x (matrix-ref bv 0 0))
(* y (matrix-ref bv 1 0))
(matrix-ref bv 3 0))
(+ (* x (matrix-ref bv 0 1))
(* y (matrix-ref bv 1 1))
(matrix-ref bv 3 1)))))
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