93 lines
3.1 KiB
Python
93 lines
3.1 KiB
Python
import Image as img
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import numpy as np
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import pylab as pl
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n = 3
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GridI, GridJ = np.meshgrid(np.linspace(-1, 1, n), np.linspace(-1, 1, n))
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img = np.ones((n,n))
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# constant factor of Ylm
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c00 = 0.282095
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c1minus1 = 0.488603
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c10 = 0.488603
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c11 = 0.488603
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c2minus2 = 1.092548
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c2minus1 = 1.092548
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c21 = 1.092548
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c20 = 0.315392
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c22 = 0.546274
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def computeYmlOnGrid(Xgrid, Ygrid, Zgrid):
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"compute Yml from Y00 to Y22 on Xgrid/Ygrid/Zgrid"
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norm = np.sqrt(Xgrid * Xgrid + Ygrid * Ygrid + Zgrid * Zgrid)
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Xg = Xgrid / norm
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Yg = Ygrid / norm
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Zg = Zgrid / norm
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Y00 = c00
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Y1minus1 = c1minus1 * Yg
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Y10 = c10 * Zg
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Y11 = c11 * Xg
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Y2minus2 = c2minus2 * Xg * Yg
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Y2minus1 = c2minus1 * Yg * Zg
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Y21= c21 * Xg * Zg
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Y20 = c20 * (3 * Zg * Zg - 1)
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Y22 = c22 * (Xg * Xg - Yg * Yg)
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return (Y00, Y1minus1, Y10, Y11, Y2minus2, Y2minus1, Y20, Y21, Y22)
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# From http://www.rorydriscoll.com/2012/01/15/cubemap-texel-solid-angle/
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def areaToPoint(x, y):
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return np.arctan2(x * y, np.sqrt(x * x + y * y + 1))
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def getSolidAngleGrid(Xgrid, Ygrid):
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"Compute solid angles using Xgrid/Ygrid/Zgrid texel position"
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(step, _) = np.shape(Xgrid)
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x0 = Xgrid - (1. / step)
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x1 = Xgrid + (1. / step)
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y0 = Ygrid - (1. / step)
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y1 = Ygrid + (1. / step)
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return areaToPoint(x0,y0) - areaToPoint(x1, y0) - areaToPoint(x0, y1) + areaToPoint(x1, y1)
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def computeCoefficients():
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"Compute coefficient SH00 to SH22 for monochromatic img"
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FaceGrid = [(np.ones((n,n)), -GridI, -GridJ), #GL_TEXTURE_CUBE_MAP_POSITIVE_X
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(-1 * np.ones((n,n)), -GridI, GridJ), #GL_TEXTURE_CUBE_MAP_NEGATIVE_X
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(GridJ, np.ones((n,n)), GridI), #GL_TEXTURE_CUBE_MAP_POSITIVE_Y
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(GridJ, -1 * np.ones((n,n)), -GridI), #GL_TEXTURE_CUBE_MAP_NEGATIVE_Y
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(GridJ, GridI, np.ones((n,n))), #GL_TEXTURE_CUBE_MAP_POSITIVE_Z
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(GridJ, -GridI, -1 * np.ones((n,n)))] #GL_TEXTURE_CUBE_MAP_NEGATIVE_Z
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incomingIrradiance = getSolidAngleGrid(GridI, GridJ)
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SH00 = 0
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SH1minus1 = 0
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SH10 = 0
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SH11 = 0
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SH2minus2 = 0
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SH2minus1 = 0
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SH20 = 0
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SH21 = 0
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SH22 = 0
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for (Xgrid, Ygrid, Zgrid) in FaceGrid:
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(Y00, Y1minus1, Y10, Y11, Y2minus2, Y2minus1, Y20, Y21, Y22) = computeYmlOnGrid(Xgrid, Ygrid, Zgrid)
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SH00 += np.sum(Y00 * incomingIrradiance * img)
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SH1minus1 += np.sum(Y1minus1 * incomingIrradiance * img)
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SH10 += np.sum(Y10 * incomingIrradiance * img)
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SH11 += np.sum(Y11 * incomingIrradiance * img)
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SH2minus2 += np.sum(Y2minus2 * incomingIrradiance * img)
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SH2minus1 += np.sum(Y2minus1 * incomingIrradiance * img)
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SH20 += np.sum(Y20 * incomingIrradiance * img)
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SH21 += np.sum(Y21 * incomingIrradiance * img)
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SH22 += np.sum(Y22 * incomingIrradiance * img)
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return (SH00, SH1minus1, SH10, SH2minus2, SH2minus1, SH20, SH21, SH22)
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print(computeCoefficients())
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#res = []
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#for (Xd, Yd, Zd) in FaceGrid:
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# res.append(computeYmlOnGrid(Xd, Yd, Zd))
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#I = img.open("C:/Users/vljn_000/Documents/GitHub/stk-assets/textures/ants.png")
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#m = np.array(I)
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#print(type(m))
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#pl.imshow(m)
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