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import math, sys
from PIL import Image
W, H = 640, 480
FILL = (0, 0, 0)
fb = None
def fixed_color(color):
for c in color[:3]:
c = abs(int(c * (1 << 8)))
yield (c & 255) | (255 if (c & (1 << 8)) else 0)
def fixed(p):
pos, color = p
w = pos
pos = tuple(int(c / pos[3] * (1 << 13)) for c in pos[:3])
return (pos, tuple(fixed_color(color)))
def bounding(p0, p1, p2):
minx = max(min(p0[0][0], p1[0][0], p2[0][0]), (-W // 2) << 4)
maxx = min(max(p0[0][0], p1[0][0], p2[0][0]), (W // 2) << 4)
miny = max(min(p0[0][1], p1[0][1], p2[0][1]), (-H // 2) << 4)
maxy = min(max(p0[0][1], p1[0][1], p2[0][1]), (H // 2) << 4)
return (minx, miny, maxx, maxy)
def edge_fn(p, q, sx, sy):
p, q = p[0], q[0]
# https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/rasterization-stage.html
a, b = p[1] - q[1], -(p[0] - q[0])
r = (sx - q[0]) * a + (sy - q[1]) * b
return r, r, a, b
def raster(p0, p1, p2, msaa=True):
global fb
# https://math.stackexchange.com/questions/1324179/how-to-tell-if-3-connected-points-are-connected-clockwise-or-counter-clockwise
A = p1[0][0] * p0[0][1] + p2[0][0] * p1[0][1] + p0[0][0] * p2[0][1]
B = p0[0][0] * p1[0][1] + p1[0][0] * p2[0][1] + p2[0][0] * p0[0][1]
if A > B:
p1, p2 = p2, p1
minx, miny, maxx, maxy = bounding(p0, p1, p2)
sx, sy = minx // 16 * 16, miny // 16 * 16
base_x_a, base_y_a, add_x_a, add_y_a = edge_fn(p0, p1, sx, sy)
base_x_b, base_y_b, add_x_b, add_y_b = edge_fn(p1, p2, sx, sy)
base_x_c, base_y_c, add_x_c, add_y_c = edge_fn(p2, p0, sx, sy)
int_x_a = add_x_a << 4
int_x_b = add_x_b << 4
int_x_c = add_x_c << 4
int_y_a = add_y_a << 4
int_y_b = add_y_b << 4
int_y_c = add_y_c << 4
if msaa:
samples = ((-5, 10), (11, 2), (-7, -4))
else:
samples = ((0, 0),)
samples_a = tuple(add_x_a * sx + add_y_a * sy for sx, sy in samples)
samples_b = tuple(add_x_b * sx + add_y_b * sy for sx, sy in samples)
samples_c = tuple(add_x_c * sx + add_y_c * sy for sx, sy in samples)
for x in range(minx // 16 * 16, maxx + 16, 16):
for y in range(miny // 16 * 16, maxy + 16, 16):
count = 0
for a, b, c in zip(samples_a, samples_b, samples_c):
if base_y_a + a >= 0 and base_y_b + b >= 0 and base_y_c + c >= 0:
count += 1
if count > 0:
yield (x >> 4, y >> 4, count if msaa else 3)
base_y_a += int_y_a
base_y_b += int_y_b
base_y_c += int_y_c
base_x_a += int_x_a
base_x_b += int_x_b
base_x_c += int_x_c
base_y_a = base_x_a
base_y_b = base_x_b
base_y_c = base_x_c
def translate(x, y, z):
return ((1, 0, 0, x),
(0, 1, 0, y),
(0, 0, 1, z),
(0, 0, 0, 1))
def scale(x, y, z):
return ((x, 0, 0, 0),
(0, y, 0, 0),
(0, 0, z, 0),
(0, 0, 0, 1))
def rotate(x, y, z, angle):
mag = math.hypot(x, y, z)
x /= mag
y /= mag
z /= mag
angle = math.radians(angle)
c, s = math.cos(angle), math.sin(angle)
return ((x * x * (1 - c) + c, x * y * (1 - c) - z * s, x * z * (1 - c) + y * s, 0),
(y * x * (1 - c) + z * s, y * y * (1 - c) + c, y * z * (1 - c) - x * s, 0),
(x * z * (1 - c) - y * s, y * z * (1 - c) + x * s, z * z * (1 - c) + c, 0),
(0, 0, 0, 1))
def frustum(left, right, bottom, top, near, far):
# https://docs.gl/gl3/glFrustum
l, r, b, t, n, f = left, right, bottom, top, near, far
return ((2 * n / (r - l), 0, (r + l) / (r - l), 0),
(0, 2 * n / (t - b), (t + b) / (t - b), 0),
(0, 0, -(f + n) / (f - n), -2 * f * n / (f - n)),
(0, 0, -1 , 0))
def mat_mat(a, b):
n = lambda: range(len(a))
return tuple(tuple(sum(a[i][k] * b[k][j] for k in n()) for j in n()) for i in n())
def mat_vec(mat, vec):
return tuple(sum(a * b for a, b in zip(r, vec)) for r in mat)
def backend(a, f, w):
tri = (((-1.0, -1.0, 1, 1.0), (1.0, 0.0, 0.0, 0.0)),
(( 1.0, -1.0, 1, 1.0), (0.0, 1.0, 0.0, 0.0)),
(( 0.0, 1.0, 3, 1.0), (0.0, 0.0, 1.0, 0.0)))
m = frustum(-w, w, -w, w, -5, 5)
m = mat_mat(m, rotate(1, 0, 0, a))
m = mat_mat(m, scale(f, f, f))
tri = tuple((mat_vec(m, p), c) for p, c in tri)
tri = tuple(fixed(p) for p in tri)
for x, y, frac in raster(*tri):
if -W // 2 <= x < W // 2 and -H // 2 <= y < H // 2:
x += W // 2
y = H // 2 - y - 1
fb[y * W + x] = (255 * frac // 3, 255 * frac // 3, 255 * frac // 3)
imgs = []
def do_frame(a, f, w):
global fb, imgs
fb = [FILL] * W * H
backend(a, f, w)
image = Image.new('RGB', (W, H))
image.putdata(fb)
imgs.append(image)
a, f, w = int(sys.argv[1]), float(sys.argv[2]), float(sys.argv[3])
for n in range(100):
do_frame(n * a, f, w)
imgs[0].save('out.gif',
save_all=True,
append_images=imgs[1:],
duration=100,
loop=0)
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