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intersect.py
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intersect.py
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from numpy import *
from interp import *
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import pylab
import time
def triray_inter(P0,rd,V0,V1,V2):
# determine if a ray intersects a triangle
# inputs
# P0 : starting point of ray
# rd : direction of ray
# V0,V1,V2 : vertices of triangle
# o V2
# /^
# / | v,y
# / |
# / |
# V1 o<---o V0
# u,x
# returns
# x,y : parametric location of intersection
# PI : x,y,z coordinates of intersection
u = V1 - V0
v = V2 - V0
n = cross(u,v)
w0 = P0 - V0
a = -dot(n,w0)
b = dot(n,rd)
r = a / b
# intersection of line and plane
PI = P0 + r*rd
uu = dot(u,u)
uv = dot(u,v)
vv = dot(v,v)
w = PI - V0
wu = dot(w,u)
wv = dot(w,v)
den = uv*uv - uu*vv
# outside if x < 0 or x > 1
x = (uv*wv - vv*wu)/den
if (x < 0.0 or x > 1.0):
return 0,0,0,0
# outside if y < 0 or (x+y) > 1
y = (uv*wu - uu*wv)/den
if (y < 0.0 or (x+y) > 1.0):
return 0,0,0,0
return 1,x,y,PI
def uv_inter(P0,rd,u0,u1,v0,v1,k,l,s,t,P):
# 4 3
# (u0,v1) o----o (u1,v1)
# | /|
# | / |
# | / |
# |/ |
# (u0,v0) o----o (u1,v0)
# 1 2
#
# o V2
# /^
# / |
# / |
# / |
# V1 o<---o V0
#
# V0 o--->o V2
# | /
# | /
# | /
# V/
# V1 o
# check intersection with triangle 1-2-3
V0 = eval_surf(k,l,s,t,P,u1,v0)
V1 = eval_surf(k,l,s,t,P,u0,v0)
V2 = eval_surf(k,l,s,t,P,u1,v1)
I,x,y,PI = triray_inter(P0,rd,V0,V1,V2)
if I==1:
uI = u1 - x*(u1-u0)
vI = v0 + y*(v1-v0)
return 1, uI, vI, PI
# check intersection with triangle 1-3-4
if I == 0:
V0 = eval_surf(k,l,s,t,P,u0,v1)
I,x,y,PI = triray_inter(P0,rd,V0,V1,V2)
if I==1:
uI = u0 + y*(u1-u0)
vI = v1 - x*(v1-v0)
return 1, uI, vI, PI
return 0,0,0,0
def raysurf_inter(P0,rd,f,k,l,s,t,P):
# inputs
# f : factor to subdivide surf by each step
uI = vI = 0.5
w = 1.0
I = 1
err = 10e6
# subdivide until convergence
while I and (err > 1e-8):
umin = max(0.,uI - 0.5*w)
umax = min(1.,uI + 0.5*w)
vmin = max(0.,vI - 0.5*w)
vmax = min(1.,vI + 0.5*w)
ug = linspace(umin,umax,f+1)
vg = linspace(vmin,vmax,f+1)
i = I = 0
while ((not I) and (i < f)):
j = 0
while ((not I) and (j < f)):
I,uI,vI,PI = uv_inter(P0,rd,ug[i],ug[i+1],vg[j],vg[j+1],k,l,s,t,P)
j += 1
i += 1
PI_uv = eval_surf(k,l,s,t,P,uI,vI)
if I == 0:
print 'Error: No Intersection found'
w /= f
err = sqrt((PI[0]-PI_uv[0])**2 + (PI[1]-PI_uv[1])**2 + (PI[2]-PI_uv[2])**2)
return PI,uI,vI
tic = time.clock()
# construct test surface
m = 5
n = 5
Q = zeros((m+1,n+1,3))
s = linspace(0.,1.,m+1)
t = linspace(0.,1.,n+1)
Q[:,:,0], Q[:,:,1] = meshgrid(t,s)
for i in range(m+1):
for j in range(n+1):
# Q[i,j,2] = cos(6*s[i])*sin(4*t[j])*t[j]
Q[i,j,2] = (1.-s[i])*(1.-t[j])
k = l = 4
P, u, v, s, t = interp_surf(Q,k,l)
toc = time.clock()
print 'Time to construct surface : ', toc-tic
P0 = array([0.25,0.25,0.1])
rd = array([0.2,0.1,1.])
tic = time.clock()
PI,uI,vI = raysurf_inter(P0,rd,2,k,l,s,t,P)
toc = time.clock()
print 'Time to intersect : ', toc-tic
print 'uI, vI : ', uI, vI
uu = linspace(0.,1.,20)
vv = linspace(0.,1.,20)
S = zeros((len(uu),len(vv),3))
for i in range(len(uu)):
for j in range(len(vv)):
S[i,j,:] = eval_surf(k,l,s,t,P,uu[i],vv[j])
fig = pylab.figure()
ax = Axes3D(fig)
ax.plot_surface(S[:,:,0], S[:,:,1], S[:,:,2], rstride=1, cstride=1, cmap = cm.jet)
ray = vstack((P0-1*rd,P0+1*rd))
inter = vstack((PI,PI))
ax.plot(inter[:,0],inter[:,1],inter[:,2],'*')
#for i in range(m+1):
# ax.plot(Q[i,:,0],Q[i,:,1],Q[i,:,2],'k*')
ax.plot(ray[:,0],ray[:,1],ray[:,2])
pylab.show()