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;;; Copyright © 2020 Jakob L. Kreuze <zerodaysfordays@sdf.org>
;;;
;;; 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/>.
(defun make-some (n) (cons 'some n))
(defun make-none () 'none)
(defun some-p (n) (and (consp n) (eq 'some (car n))))
(defun none-p (n) (eq 'none n))
(defun unwrap (n)
(if (some-p n)
(cdr n)
(error "Tried to unwrap `none'.")))
(defun map-option (proc n)
(if (some-p n)
(make-some (funcall proc (unwrap n)))
n))
;;;
;;; Image encoding.
;;;
(defun write-ppm (width height pixels)
"Encode the WIDTH by HEIGHT image given as PIXELS into the portable pixmap
format (PPM), writing the result to `(current-output-port)'."
(write-line "P3")
(format t "~a ~a~%" width height)
(write-line "255")
(loop for (r g b) across pixels
do (format t "~a ~a ~a~%" r g b)))
;;;
;;; Are mathematical objects in the room with us right now?
;;;
(defun square (n) (* n n))
(defstruct vec3 x y z)
(defun vec3+ (&rest vecs)
"Return the sum of VECS, as in vector space addition."
(if (zerop (length vecs))
(make-vec3 :x 0 :y 0 :z 0)
(reduce #'(lambda (a b)
(with-slots ((x1 x) (y1 y) (z1 z)) a
(with-slots ((x2 x) (y2 y) (z2 z)) b
(make-vec3 :x (+ x1 x2)
:y (+ y1 y2)
:z (+ z1 z2)))))
(cdr vecs)
:initial-value (car vecs))))
(defun vec3- (&rest vecs)
"Return the difference of VECS, as in vector space subtraction."
(if (zerop (length vecs))
(make-vec3 :x 0 :y 0 :z 0)
(reduce #'(lambda (a b)
(with-slots ((x1 x) (y1 y) (z1 z)) a
(with-slots ((x2 x) (y2 y) (z2 z)) b
(make-vec3 :x (- x1 x2)
:y (- y1 y2)
:z (- z1 z2)))))
(cdr vecs)
:initial-value (car vecs))))
(defun vec3* (c u)
"Return the vector U scaled by a constant C, as in vector space scalar
multiplication."
(with-slots (x y z) u
(make-vec3 :x (* c x) :y (* c y) :z (* c z))))
(defun vec3-dot (u v)
"Return the dot product of the vectors U and V."
(+ (* (vec3-x u) (vec3-x v))
(* (vec3-y u) (vec3-y v))
(* (vec3-z u) (vec3-z v))))
(defun vec3-cross (u v)
"Return the cross product of the vectors U and V."
(with-slots ((x1 x) (y1 y) (z1 z)) u
(with-slots ((x2 x) (y2 y) (z2 z)) v
(make-vec3 :x (- (* y1 z2) (* z1 y2))
:y (- (* z1 x2) (* x1 z2))
:z (- (* x1 y2) (* y1 x2))))))
(defun vec3-magnitude (u)
"Return the magnitude of vector U."
(with-slots (x y z) u
(sqrt (+ (square x) (square y) (square z)))))
(defun vec3-normalize (u)
"Return the normal vector parallel to vector U."
(vec3* (/ 1 (vec3-magnitude u)) u))
(defstruct ray origin direction)
(defmethod point-at ((r ray) time)
"Return the position of RAY at time T."
(with-slots (origin direction) r
(vec3+ origin (vec3* time direction))))
(defun to-radians (d)
"Convert D, a value in degrees, to radians."
(* d (/ PI 360)))
;;;
;;; Shapes and generic procedures for working with them.
;;;
(defstruct plane p0 n material)
(defmethod intersect (ray (p plane) t-min t-max)
(with-slots (p0 (plane-normal n)) p
(with-slots (origin direction) ray
(let* ((normal (vec3-normalize plane-normal))
(denominator (vec3-dot direction normal)))
(if (zerop denominator)
(make-none)
(let ((time (/ (vec3-dot (vec3- p0 origin) normal)
denominator)))
(if (<= t-min time t-max)
(make-some time)
(make-none))))))))
(defstruct sphere center radius material)
(defmethod intersect (ray (s sphere) t-min t-max)
(with-slots (origin direction) ray
(with-slots (center radius) s
(let* ((oc (vec3* (- 1) (vec3- center origin)))
(A (vec3-dot direction direction))
(B (* 2.0 (vec3-dot oc direction)))
(C (- (vec3-dot oc oc) (square radius)))
(discriminant (- (square B) (* 4 A C)))
(time (if (plusp discriminant)
(let ((p (/ (+ (- B) (sqrt discriminant)) (* 2 A)))
(m (/ (- (- B) (sqrt discriminant)) (* 2 A))))
(if (>= m t-min) m p))
(/ (- B) (* 2 A)))))
(if (and (not (minusp discriminant))
(<= t-min time t-max))
(make-some time)
(make-none))))))
;;;
;;; Scene graph.
;;;
(defvar image-width 1920)
(defvar image-height 1080)
(defvar image-aspect-ratio (/ image-width image-height))
(defvar camera-position (make-vec3 :x 8.00 :y 5.00 :z 9.00))
(defvar camera-target (make-vec3 :x 0.25 :y 0.00 :z 0.50))
(defvar camera-up (make-vec3 :x 0.00 :y 1.00 :z 0.00))
(defvar camera-fov 30)
(defvar shapes (list (make-sphere :center (make-vec3 :x -0.25 :y 0.00 :z 0.25)
:radius 1.25
;; (phong-material (make-vec3 1.0 0.2 0.2)
;; (make-vec3 1.0 0.2 0.2)
;; (make-vec3 2.0 2.0 2.0)
;; 20)
:material nil
)
;; (make-plane :p0 (make-vec3 :x 0.00 :y -1.25 :z 0.00)
;; :n (make-vec3 :x 0.00 :y 1.00 :z 0.00)
;; ;; (diffuse-material (make-vec3 1.0 1.0 0.2)
;; ;; (make-vec3 1.0 1.0 0.2))
;; :material nil
;; )
))
(defun coord-to-ray (x y)
"Return the ray corresponding to the point X, Y on the viewport plane."
(let* ((dist 1.0)
(top (* dist (tan (to-radians camera-fov))))
(right (* top image-aspect-ratio))
(bottom (- top))
(left (- right))
(W (vec3-normalize (vec3- camera-position camera-target)))
(U (vec3-normalize (vec3-cross camera-up W)))
(V (vec3-cross W U))
(corner (vec3+ camera-position
(vec3* left U)
(vec3* bottom V)
(vec3* (- dist) W)))
(across (vec3* (* 2 right) U))
(up (vec3* (* 2 top) V)))
(make-ray :origin camera-position
:direction (vec3-normalize
(vec3+ corner
(vec3* x across)
(vec3* y up)
(vec3* (- 1) camera-position))))))
(defun lerp (a b time)
"Interpolate between A and B with parameter T."
(+ (* (- 1.0 time) a) (* time b)))
(defun ray-color (r)
"Return an arbitrary color for R."
(let* ((y (vec3-y (ray-direction r)))
(time (* 0.5 (+ y 1.0))))
(list (round (* 255 (lerp 1.0 0.5 time)))
(round (* 255 (lerp 1.0 0.7 time)))
(round (* 255 (lerp 1.0 1.0 time))))))
(defun ray-intersect-scene (ray)
"Return the nearest shape with which RAY intersects as (some . (shape .
point)), if any. Otherwise, return 'none."
(map-option
#'(lambda (pair)
(list (car pair) (point-at ray (cadr pair))))
(reduce #'(lambda (a b)
(cond ((none-p a) b)
((none-p b) a)
(t (let ((t1 (unwrap a))
(t2 (unwrap b)))
(if (> (cadr t1) (cadr t2)) b a)))))
(mapcar #'(lambda (shape)
(let ((intersection (intersect ray shape 0.001 10000)))
(map-option #'(lambda (time) (list shape time)) intersection)))
shapes)
:initial-value (make-none))))
(let ((image (make-array (* image-width image-height) :initial-element '(0 0 0))))
(flet ((coord-to-index (x y)
(+ x (* y image-width)))
(screen-to-viewport (x y)
(values (coerce (/ x image-width) 'real)
(coerce (/ (- image-height 1 y) image-height) 'real))))
(dotimes (x image-width)
(dotimes (y image-height)
(setf (elt image (coord-to-index x y))
(multiple-value-bind (x y) (screen-to-viewport x y)
(let ((ray (coord-to-ray x y)))
(if (some-p (ray-intersect-scene ray))
(list 0 0 0)
(ray-color ray))))))))
(write-ppm image-width image-height image))
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