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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/>.
(fn pack [...]
(var result [])
(let [n (select "#" ...)]
(for [i 1 n]
(tset result i (select i ...))))
result)
(fn fold [f init sequence]
(var result init)
(for [i 1 (# sequence)]
(set result (f result (. sequence i))))
result)
;;;
;;; Image encoding.
;;;
(fn write-ppm [image]
"Encode the WIDTH by HEIGHT image given as PIXELS into the portable pixmap
format (PPM), writing the result to standard output."
(print "P3")
(print (string.format "%d %d" image.width image.height))
(print "255")
(for [i 1 (# image.pixels)]
(let [[r g b] (. image.pixels i)]
(print (string.format "%d %d %d" r g b)))))
(fn set-pixel [image x y color]
"Set the color of the pixel at X, Y to COLOR."
(let [offset (+ 1 x (* y image.width))]
(tset image.pixels offset color)))
(fn image [width height]
"Return an image object with dimensions WIDTH by HEIGHT."
(let [pixels {}]
(for [i 1 (* width height)]
(tset pixels i [0 0 0]))
{:width width :height height :pixels pixels}))
;;;
;;; Are mathematical objects in the room with us right now?
;;;
(fn square [n] (* n n))
(fn vec3 [x y z] {:x x :y y :z z})
(fn vec3+ [...]
"Return the sum of VECS, as in vector space addition."
(fold (fn [a b]
(let [{:x α :y β :z γ} a
{:x x :y y :z z} b]
(vec3 (+ α x) (+ β y) (+ γ z))))
(vec3 0.00 0.00 0.00)
(pack ...)))
(fn vec3- [...]
"Return the difference of VECS, as in vector space subtraction."
(fold (fn [a b]
(let [{:x α :y β :z γ} a
{:x x :y y :z z} b]
(vec3 (- α x) (- β y) (- γ z))))
(vec3 0.00 0.00 0.00)
(pack ...)))
(fn vec3* [c u]
"Return the vector U scaled by a constant C, as in vector space scalar
multiplication."
(let [{:x x :y y :z z} u]
(vec3 (* c x) (* c y) (* c z))))
(fn vec3-dot [u v]
"Return the dot product of the vectors U and V."
(let [{:x α :y β :z γ} u
{:x x :y y :z z} v]
(+ (* α x) (* β y) (* γ z))))
(fn vec3-cross [u v]
"Return the cross product of the vectors U and V."
(let [{:x α :y β :z γ} u
{:x x :y y :z z} v]
(vec3 (- (* β z) (* γ y))
(- (* γ x) (* α z))
(- (* α y) (* β x)))))
(fn vec3-magnitude [u]
"Return the magnitude of vector U."
(let [{:x x :y y :z z} u]
(math.sqrt (+ (square x) (square y) (square z)))))
(fn vec3-normalize [u]
"Return the normal vector parallel to vector U."
(vec3* (/ 1 (vec3-magnitude u)) u))
(fn ray [origin direction] { :origin origin :direction direction })
(fn point-at [r t]
"Return the position of RAY at time T."
(let [{ :origin origin :direction direction } r]
(vec3+ origin (vec3* t direction))))
(fn degrees->radians [d]
"Convert D, a value in degrees, to radians."
(* d (/ math.pi 360)))
(global image-width 1920)
(global image-height 1080)
(global image-aspect-ratio (/ image-width image-height))
(global camera-position (vec3 8.00 5.00 9.00))
(global camera-target (vec3 0.25 0.00 0.50))
(global camera-up (vec3 0.00 1.00 0.00))
(global camera-fov 30)
(fn coordinate->ray [x y]
"Return the ray corresponding to the point X, Y on the viewport plane."
(let [dist 1.0
top (* dist (math.tan (degrees->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)]
(ray camera-position
(vec3-normalize
(vec3+ corner
(vec3* x across)
(vec3* y up)
(vec3* (- 1) camera-position))))))
;;;
;;; Scene graph.
;;;
(fn lerp [a b t]
"Interpolate between A and B with parameter T."
(+ (* (- 1.0 t) a) (* t b)))
(fn ray-color [r]
"Return an arbitrary color for R."
(let [{:direction direction} r
{:y y} (vec3-normalize direction)
t (* 0.5 (+ y 1.0))]
[(math.floor (* 255 (lerp 1.0 0.5 t)))
(math.floor (* 255 (lerp 1.0 0.7 t)))
(math.floor (* 255 (lerp 1.0 1.0 t)))]))
(fn screen->viewport [x y]
(values (/ x image-width)
(/ (- image-height 1 y)
image-height)))
(fn main []
(var output (image image-width image-height))
(for [x 0 image-width]
(for [y 0 image-height]
(let [r (coordinate->ray (screen->viewport x y))]
(set-pixel output x y (ray-color r)))))
(write-ppm output))
(main)
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