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-;;; guile-2d
-;;; Copyright (C) 2014 David Thompson <dthompson2@worcester.edu>
-;;;
-;;; This program 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.
-;;;
-;;; This program 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/>.
-
-;;; Commentary:
-;;
-;; 4x4 column-major transformation matrix.
-;;
-;;; Code:
-
-(define-module (2d transform)
- #:use-module (srfi srfi-1)
- #:use-module (srfi srfi-9)
- #:use-module (srfi srfi-42)
- #:use-module (2d math)
- #:use-module (2d vector)
- #:export (make-transform null-transform identity-transform
- transform? transform-matrix
- transpose transform-vector2
- transform+ transform*
- scale translate rotate-x rotate-y rotate-z
- orthographic-projection perspective-projection))
-
-(define-record-type <transform>
- (%make-transform matrix)
- transform?
- (matrix transform-matrix))
-
-(define (make-4x4-matrix)
- (make-typed-array 'f32 0 4 4))
-
-(define (make-transform aa ab ac ad
- ba bb bc bd
- ca cb cc cd
- da db dc dd)
- "Return a new transform initialized with the given 16 values in
-column-major format."
- (let ((matrix (make-4x4-matrix)))
- (array-set! matrix aa 0 0)
- (array-set! matrix ab 0 1)
- (array-set! matrix ac 0 2)
- (array-set! matrix ad 0 3)
- (array-set! matrix ba 1 0)
- (array-set! matrix bb 1 1)
- (array-set! matrix bc 1 2)
- (array-set! matrix bd 1 3)
- (array-set! matrix ca 2 0)
- (array-set! matrix cb 2 1)
- (array-set! matrix cc 2 2)
- (array-set! matrix cd 2 3)
- (array-set! matrix da 3 0)
- (array-set! matrix db 3 1)
- (array-set! matrix dc 3 2)
- (array-set! matrix dd 3 3)
- (%make-transform matrix)))
-
-(define null-transform
- (%make-transform (make-4x4-matrix)))
-
-(define identity-transform
- (make-transform 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- 0 0 0 1))
-
-(define (transpose transform)
- "Return a transform that is the transpose of TRANSFORM."
- (let ((m1 (transform-matrix transform))
- (m2 (make-4x4-matrix)))
- (do-ec (: r 4) (: c 4)
- (array-set! m2 (array-ref m1 r c)
- c r))
- (%make-transform m2)))
-
-(define (transform-vector2 transform v)
- "Apply TRANSFORM to the 2D vector V."
- (let ((m (transform-matrix transform))
- (x (vx v))
- (y (vy v)))
- (vector (+ (* x (array-ref m 0 0))
- (* y (array-ref m 0 1))
- (array-ref m 0 3))
- (+ (* x (array-ref m 1 0))
- (* y (array-ref m 1 1))
- (array-ref m 1 3)))))
-
-(define (transform+ . transforms)
- "Return the sum of all given transformation matrices. Return
-null-transform if called without any arguments."
- (define (add a b)
- (let ((m1 (transform-matrix a))
- (m2 (transform-matrix b))
- (m3 (make-4x4-matrix)))
- (do-ec (: r 4) (: c 4)
- (let ((x (+ (array-ref m1 r c)
- (array-ref m2 r c))))
- (array-set! m3 x r c)))
- (%make-transform m3)))
- (reduce add null-transform transforms))
-
-(define (transform* . transforms)
- "Return the product of all given transformation matrices. Return
-identity-transform if called without any arguments."
- (define (mul a b)
- (let ((m1 (transform-matrix a))
- (m2 (transform-matrix b))
- (m3 (make-4x4-matrix)))
- (do-ec (: r 4) (: c 4)
- (let ((x (sum-ec (: k 4)
- (* (array-ref m1 r k)
- (array-ref m2 k c)))))
- (array-set! m3 x r c)))
- (%make-transform m3)))
- (reduce mul identity-transform transforms))
-
-(define (translate v)
- "Return a new transform that translates by the 2D or 3D vector V."
- (cond
- ((vector2? v)
- (let ((x (vx v))
- (y (vy v)))
- (make-transform 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- x y 0 1)))
- ((vector3? v)
- (let ((x (vx v))
- (y (vy v))
- (z (vz v)))
- (make-transform 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- x y z 1)))
- (else
- (error "Invalid scaling vector: " v))))
-
-(define (scale v)
- "Return a new transform that scales by the 2D vector, 3D vector, or
-scalar V."
- (cond
- ((number? v)
- (make-transform v 0 0 0
- 0 v 0 0
- 0 0 v 0
- 0 0 0 1))
- ((vector2? v)
- (let ((x (vx v))
- (y (vy v)))
- (make-transform x 0 0 0
- 0 y 0 0
- 0 0 1 0
- 0 0 0 1)))
- ((vector3? v)
- (let ((x (vx v))
- (y (vy v))
- (z (vz v)))
- (make-transform x 0 0 0
- 0 y 0 0
- 0 0 z 0
- 0 0 0 1)))
- (else
- (error "Invalid scaling vector: " v))))
-
-(define (rotate-x angle)
- "Return a new transform that rotates the X axis by ANGLE radians."
- (make-transform 1 0 0 0
- 0 (cos angle) (- (sin angle)) 0
- 0 (sin angle) (cos angle) 0
- 0 0 0 1))
-
-(define (rotate-y angle)
- "Return a new transform that rotates the Y axis by ANGLE radians."
- (make-transform (cos angle) 0 (sin angle) 0
- 0 1 0 0
- (- (sin angle)) 0 (cos angle) 0
- 0 0 0 1))
-(define (rotate-z angle)
- "Return a new transform that rotates the Z axis by ANGLE radians."
- (make-transform (cos angle) (- (sin angle)) 0 0
- (sin angle) (cos angle) 0 0
- 0 0 1 0
- 0 0 0 1))
-
-(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-transform (/ 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 (perspective-projection field-of-vision aspect-ratio near far)
- "Return a new transform that represents a perspective projection
-with a FIELD-OF-VISION in degrees, the desired ASPECT-RATIO, and the
-depth clipping plane NEAR and FAR."
- (let ((size (* near (tan (/ (degrees->radians field-of-vision) 2)))))
- (let ((left (- size))
- (right size)
- (top (/ size aspect-ratio))
- (bottom (/ (- size) aspect-ratio)))
- (make-transform (/ (* 2 near) (- right left)) ;; First row
- 0
- (/ (+ right left) (- right left))
- 0
- ;; Second row
- 0
- (/ (* 2 near) (- top bottom))
- (/ (+ top bottom) (- top bottom))
- 0
- ;; Third row
- 0 0
- (- (/ (+ far near) (- far near)))
- (- (/ (* 2 far near) (- far near)))
- ;; Fourth row
- 0 0 -1 0))))
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