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[example] Update quaternion arithmetics in fractal_3d_ggui #7139

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Jan 13, 2023
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[example] Update quaternion arithmetics in fractal_3d_ggui #7139

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136 changes: 41 additions & 95 deletions python/taichi/examples/ggui_examples/fractal3d_ggui.py
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Original file line number Diff line number Diff line change
@@ -1,62 +1,22 @@
import taichi as ti
import taichi.math as tm

arch = ti.vulkan if ti._lib.core.with_vulkan() else ti.cuda
ti.init(arch=arch)

vec3 = tm.vec3
vec4 = tm.vec4


@ti.func
def quat_mul(v1, v2):
return ti.Vector([
v1.x * v2.x - v1.y * v2.y - v1.z * v2.z - v1.w * v2.w,
v1.x * v2.y + v1.y * v2.x + v1.z * v2.w - v1.w * v2.z,
v1.x * v2.z + v1.z * v2.x + v1.w * v2.y - v1.y * v2.w,
v1.x * v2.w + v1.w * v2.x + v1.y * v2.z - v1.z * v2.y
])
return vec4(v1.x * v2.x - tm.dot(v1.yzw, v2.yzw),
v1.x * v2.yzw + v2.x * v1.yzw + tm.cross(v1.yzw, v2.yzw))


@ti.func
def quat_conj(q):
return ti.Vector([q[0], -q[1], -q[2], -q[3]])


@ti.func
def dot(x, y):
return x.dot(y)


@ti.func
def xy(v):
return ti.Vector([v.x, v.y])


@ti.func
def yx(v):
return ti.Vector([v.y, v.x])


@ti.func
def xz(v):
return ti.Vector([v.x, v.z])


@ti.func
def zx(v):
return ti.Vector([v.z, v.x])


@ti.func
def xw(v):
return ti.Vector([v.x, v.w])


@ti.func
def wx(v):
return ti.Vector([v.w, v.x])


@ti.func
def xyz(v):
return ti.Vector([v.x, v.y, v.z])
return vec4(q.x, -q.yzw)


iters = 10
Expand All @@ -67,7 +27,7 @@ def xyz(v):
def compute_sdf(z, c):

md2 = 1.0
mz2 = dot(z, z)
mz2 = tm.dot(z, z)

for _ in range(iters):
md2 *= max_norm * mz2
Expand All @@ -82,41 +42,28 @@ def compute_sdf(z, c):

@ti.func
def compute_normal(z, c):
J0 = ti.Vector([1.0, 0.0, 0.0, 0.0])
J1 = ti.Vector([0.0, 1.0, 0.0, 0.0])
J2 = ti.Vector([0.0, 0.0, 1.0, 0.0])
J0 = vec4(1, 0, 0, 0)
J1 = vec4(0, 1, 0, 0)
J2 = vec4(0, 0, 1, 0)

z_curr = z

iterations = 0
while z_curr.norm() < max_norm and iterations < iters:
cz = quat_conj(z_curr)

J0 = ti.Vector([
dot(J0, cz),
dot(xy(J0), yx(z_curr)),
dot(xz(J0), zx(z_curr)),
dot(xw(J0), wx(z_curr))
])
J1 = ti.Vector([
dot(J1, cz),
dot(xy(J1), yx(z_curr)),
dot(xz(J1), zx(z_curr)),
dot(xw(J1), wx(z_curr))
])
J2 = ti.Vector([
dot(J2, cz),
dot(xy(J2), yx(z_curr)),
dot(xz(J2), zx(z_curr)),
dot(xw(J2), wx(z_curr))
])
J0 = vec4(tm.dot(J0, cz), tm.dot(J0.xy, z_curr.yx),
tm.dot(J0.xz, z_curr.zx), tm.dot(J0.xw, z_curr.wx))
J1 = vec4(tm.dot(J1, cz), tm.dot(J1.xy, z_curr.yx),
tm.dot(J1.xz, z_curr.zx), tm.dot(J1.xw, z_curr.wx))
J2 = vec4(tm.dot(J2, cz), tm.dot(J2.xy, z_curr.yx),
tm.dot(J2.xz, z_curr.zx), tm.dot(J2.xw, z_curr.wx))

z_curr = quat_mul(z_curr, z_curr) + c
iterations += 1

return ti.Vector([dot(J0, z_curr),
dot(J1, z_curr),
dot(J2, z_curr)]).normalized()
return tm.normalize(
tm.vec3(tm.dot(z_curr, J0), tm.dot(z_curr, J1), tm.dot(z_curr, J2)))


image_res = (1280, 720)
Expand All @@ -130,39 +77,40 @@ def __init__(self):
@ti.func
def shade(self, pos, surface_color, normal, light_pos):
_ = self # make pylint happy
light_color = ti.Vector([1, 1, 1])
light_color = vec3(1)

light_dir = (light_pos - pos).normalized()
return light_color * surface_color * max(0, dot(light_dir, normal))
light_dir = tm.normalize(light_pos - pos)
return light_color * surface_color * ti.max(0, tm.dot(
light_dir, normal))

@ti.kernel
def march(self, time_arg: float):
time = time_arg * 0.15
c = 0.45 * ti.cos(
ti.Vector([0.5, 3.9, 1.4, 1.1]) + time *
ti.Vector([1.2, 1.7, 1.3, 2.5])) - ti.Vector([0.3, 0.0, 0.0, 0.0])
vec4(0.5, 3.9, 1.4, 1.1) + time * vec4(1.2, 1.7, 1.3, 2.5)) - vec4(
0.3, 0, 0, 0)

r = 1.8
o3 = ti.Vector([
r * ti.cos(0.3 + 0.37 * time), 0.3 +
0.8 * r * ti.cos(1.0 + 0.33 * time), r * ti.cos(2.2 + 0.31 * time)
]).normalized() * r
ta = ti.Vector([0.0, 0.0, 0.0])
o3 = tm.normalize(
vec3(r * ti.cos(0.3 + 0.37 * time),
0.3 + 0.8 * r * ti.cos(1.0 + 0.33 * time),
r * ti.cos(2.2 + 0.31 * time))) * r
ta = vec3(0)
cr = 0.1 * ti.cos(0.1 * time)

for x, y in self.image:
p = (-ti.Vector([image_res[0], image_res[1]]) +
2.0 * ti.Vector([x, y])) / (image_res[1] * 0.75)
p = (-tm.vec2(image_res) + 2.0 * tm.vec2(x, y)) / (image_res[1] *
0.75)

cw = (ta - o3).normalized()
cp = ti.Vector([ti.sin(cr), ti.cos(cr), 0.0])
cu = cw.cross(cp).normalized()
cv = cu.cross(cw).normalized()
cw = tm.normalize(ta - o3)
cp = vec3(ti.sin(cr), ti.cos(cr), 0)
cu = tm.normalize(cw.cross(cp))
cv = tm.normalize(cu.cross(cw))

d3 = (p.x * cu + p.y * cv + 2.0 * cw).normalized()
d3 = tm.normalize(p.x * cu + p.y * cv + 2.0 * cw)

o = ti.Vector([o3.x, o3.y, o3.z, 0.0])
d = ti.Vector([d3.x, d3.y, d3.z, 0.0])
o = vec4(o3, 0)
d = vec4(d3, 0)

max_t = 10

Expand All @@ -174,8 +122,8 @@ def march(self, time_arg: float):
break
if t < max_t:
normal = compute_normal(o + t * d, c)
color = abs(xyz(o + t * d)) / 1.3
pos = xyz(o + t * d)
color = abs((o + t * d).xyz) / 1.3
pos = (o + t * d).xyz
self.image[x, y] = self.shade(pos, color, normal, o3)
else:
self.image[x, y] = (0, 0, 0)
Expand All @@ -195,9 +143,7 @@ def main():

while window.running:
frame_id += 1

canvas.set_image(julia.get_image(frame_id / 60))

window.show()


Expand Down