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import numpy as np |
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from math import sqrt |
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def normalize(x, y, z): |
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unit = sqrt(x * x + y * y + z * z) |
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if unit == 0: |
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return 0, 0, 0 |
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return x / unit, y / unit, z / unit |
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def get_min_max(a, b, c): |
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min = a |
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max = a |
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if min > b: |
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min = b |
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if min > c: |
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min = c |
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if max < b: |
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max = b |
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if max < c: |
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max = c |
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return int(min), int(max) |
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def dot_product(a0, a1, a2, b0, b1, b2): |
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r = a0 * b0 + a1 * b1 + a2 * b2 |
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return r |
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def cross_product(a0, a1, a2, b0, b1, b2): |
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x = a1 * b2 - a2 * b1 |
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y = a2 * b0 - a0 * b2 |
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z = a0 * b1 - a1 * b0 |
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return x,y,z |
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def generate_faces(triangles, width, height): |
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""" draw the triangle faces with z buffer |
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Args: |
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triangles: groups of vertices |
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FYI: |
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* zbuffer, https://github.com/ssloy/tinyrenderer/wiki/Lesson-3:-Hidden-faces-removal-(z-buffer) |
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* uv mapping and perspective correction |
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""" |
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i, j, k, length = 0, 0, 0, 0 |
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bcy, bcz, x, y, z = 0.,0.,0.,0.,0. |
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a, b, c = [0.,0.,0.],[0.,0.,0.],[0.,0.,0.] |
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m, bc = [0.,0.,0.],[0.,0.,0.] |
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uva, uvb, uvc = [0.,0.],[0.,0.],[0.,0.] |
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minx, maxx, miny, maxy = 0,0,0,0 |
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length = triangles.shape[0] |
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zbuffer = {} |
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faces = [] |
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for i in range(length): |
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a = triangles[i, 0, 0], triangles[i, 0, 1], triangles[i, 0, 2] |
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b = triangles[i, 1, 0], triangles[i, 1, 1], triangles[i, 1, 2] |
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c = triangles[i, 2, 0], triangles[i, 2, 1], triangles[i, 2, 2] |
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uva = triangles[i, 0, 3], triangles[i, 0, 4] |
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uvb = triangles[i, 1, 3], triangles[i, 1, 4] |
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uvc = triangles[i, 2, 3], triangles[i, 2, 4] |
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minx, maxx = get_min_max(a[0], b[0], c[0]) |
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miny, maxy = get_min_max(a[1], b[1], c[1]) |
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pixels = [] |
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for j in range(minx, maxx + 2): |
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for k in range(miny - 1, maxy + 2): |
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x = j |
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y = k |
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m[0], m[1], m[2] = cross_product(c[0] - a[0], b[0] - a[0], a[0] - x, c[1] - a[1], b[1] - a[1], a[1] - y) |
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if abs(m[2]) > 0: |
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bcy = m[1] / m[2] |
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bcz = m[0] / m[2] |
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bc = (1 - bcy - bcz, bcy, bcz) |
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else: |
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continue |
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if bc[0] < -0.00001 or bc[1] < -0.00001 or bc[2] < -0.00001: |
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continue |
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z = 1 / (bc[0] / a[2] + bc[1] / b[2] + bc[2] / c[2]) |
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v = (uva[0] * bc[0] / a[2] + uvb[0] * bc[1] / b[2] + uvc[0] * bc[2] / c[2]) * z * width |
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u = height - (uva[1] * bc[0] / a[2] + uvb[1] * bc[1] / b[2] + uvc[1] * bc[2] / c[2]) * z * height |
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idx = ((x + y) * (x + y + 1) + y) / 2 |
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if zbuffer.get(idx) is None or zbuffer[idx] < z: |
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zbuffer[idx] = z |
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pixels.append((i, j, k, int(u) - 1, int(v) - 1)) |
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faces.append(pixels) |
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return faces |
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