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testcode_intersection.py
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#Line-plane intersection
#By Tim Sheerman-Chase
#This software may be reused under the CC0 license
#Based on http://geomalgorithms.com/a05-_intersect-1.html
from __future__ import print_function
import numpy as np
import math
deg2Rad = math.pi/180
rad2Deg = 180/math.pi
def eulerAnglesToRotationMatrix(theta):
R_x = np.array([[1, 0, 0],
[0, math.cos(theta[0]), -math.sin(theta[0])],
[0, math.sin(theta[0]), math.cos(theta[0])]])
R_y = np.array([[math.cos(theta[1]), 0, math.sin(theta[1])],
[0, 1, 0],
[-math.sin(theta[1]), 0, math.cos(theta[1])]])
R_z = np.array([[math.cos(theta[2]), -math.sin(theta[2]), 0],
[math.sin(theta[2]), math.cos(theta[2]), 0],
[0, 0, 1]])
R = np.dot(R_z, np.dot(R_y, R_x))
return R
def rotationMatrixToEulerAngles(R):
sy = math.sqrt(R[0, 0] * R[0, 0] + R[1, 0] * R[1, 0])
singular = sy < 1e-6
if not singular:
x = math.atan2(R[2, 1], R[2, 2])
y = math.atan2(-R[2, 0], sy)
z = math.atan2(R[1, 0], R[0, 0])
else:
x = math.atan2(-R[1, 2], R[1, 1])
y = math.atan2(-R[2, 0], sy)
z = 0
return np.array([x, y, z])
def line_plane_collision(planeNormal, planePoint, rayDirection, rayPoint, epsilon=1e-6):
ndotu = planeNormal.dot(rayDirection)
if abs(ndotu) < epsilon:
raise RuntimeError("no intersection or line is within plane")
w = rayPoint - planePoint
si = -planeNormal.dot(w) / ndotu
Psi = w + si * rayDirection + planePoint
return Psi
# /**
# * Determines the point of intersection between a plane defined by a point and a normal vector and a line defined by a point and a direction vector.
# *
# * @param planePoint A point on the plane.
# * @param planeNormal The normal vector of the plane.
# * @param linePoint A point on the line.
# * @param lineDirection The direction vector of the line.
# * @return The point of intersection between the line and the plane, null if the line is parallel to the plane.
# */
def lineIntersection(planePoint, planeNormal, linePoint, lineDirection):
line_unitvec = lineDirection
# line_unitvec = lineDirection / np.linalg.norm(lineDirection)
# if (planeNormal.dot(np.linalg.norm(lineDirection)) == 0):
# return "NULL"
#
# t = (planeNormal.dot(planePoint) - planeNormal.dot(linePoint)) / planeNormal.dot(np.linalg.norm(lineDirection))
# print('t', t)
# return linePoint + np.linalg.norm(lineDirection) * t
print(np.linalg.norm(lineDirection))
print(np.dot(planeNormal, lineDirection/np.linalg.norm(lineDirection)))
if (planeNormal.dot(line_unitvec) == 0):
return "NULL"
t = (planeNormal.dot(planePoint) - planeNormal.dot(linePoint)) / planeNormal.dot(line_unitvec)
print('t', t)
return linePoint + (line_unitvec * t)
def lineIntersection2(planePoint, planeNormal, linePoint, lineDirection):
# //ax × bx + ay × by
if (planeNormal[0] * lineDirection[0] + planeNormal[1] * lineDirection[1] == 0):
return "NULL"
# // Ref for dot product calculation: https://www.mathsisfun.com/algebra/vectors-dot-product.html
dot2 = (planeNormal[0] * planePoint[0] + planeNormal[1] * planePoint[1])
dot3 = (planeNormal[0] * linePoint[0] + planeNormal[1] * linePoint[1])
dot4 = (planeNormal[0] * lineDirection[0] + planeNormal[1] * lineDirection[1])
t = (dot2 - dot3) / dot4
print('t',t)
return linePoint + lineDirection * t
def is_sameside_on_line(a, b, p, q):
print('\na',a, 'b',b,'p',p,'q',q)
# x = (b - a) * (p - a)
# y = (b - a) * (q - a)
# print('x',x,'y',y, 'x @ y >= 0',x @ y, x @ y >= 0)
c1 = np.cross(b - a, p - a)
c2 = np.cross(b - a, q - a)
print('c1',c1,'c2',c2, 'c1*c2 >= 0',c1 * c2 , np.dot(c1,c2), np.dot(c1,c2) >= 0)
print('')
return np.dot(c1, c2) >= 0
def normal_vector_from_plane(p0, p1, p2):
return np.cross((p2 - p0), (p1 - p2)) / np.linalg.norm(np.cross((p2 - p0), (p1 - p2)))
def is_inside_triangle(a, b, c, p):
# print(is_sameside_on_line(a, b, c, p))
# print(is_sameside_on_line(b, c, a, p))
# print(is_sameside_on_line(c, a, b, p))
# print(all([is_sameside_on_line(a, b, c, p),
# is_sameside_on_line(b, c, a, p),
# is_sameside_on_line(c, a, b, p)]))
xs = (a, b, c) * 2
# print(xs)
# print(xs[i:i+3] for i in range(3))
# print(all(is_sameside(*xs[i:i+3], p) for i in range(3)))
# return 'NULL'
return all(is_sameside_on_line(*xs[i:i+3], p) for i in range(3))
def is_inside_plane(a, b, c, d, p):
# print(is_sameside_on_line(a, b, c, p))
# print(is_sameside_on_line(a, d, b, p))
# print(is_sameside_on_line(c, b, a, p))
# print(is_sameside_on_line(c, d, a, p))
# xs = (a, b, c, d) * 2
# print(xs)
# # print(xs[i:i+3] for i in range(3))
# # print(all(is_sameside_on_line(*xs[i:i+3], p) for i in range(3)))
# # return 'NULL'
return all([is_sameside_on_line(a, b, c, p),is_sameside_on_line(a, d, b, p),
is_sameside_on_line(c, b, a, p),is_sameside_on_line(c, d, a, p)])
def is_same_on_plane(p0, p1, p2, pnt, epsilon=3):
tnormal_basic_plane = normal_vector_from_plane(p0,p1,p2)
tnormal_test_plane = normal_vector_from_plane(p0,p1,pnt)
print(" tnormal_basic_plane",tnormal_basic_plane,"\n tnormal_test_plane",tnormal_test_plane)
print(" ",np.round(tnormal_basic_plane,epsilon) == np.round(tnormal_test_plane,epsilon))
# print(" ",all(np.round(tnormal_basic_plane,epsilon) == np.round(tnormal_test_plane,epsilon)))
# print(np.dot(tnormal_basic_plane,tnormal_test_plane))
print(" ",np.round(np.dot(tnormal_basic_plane, tnormal_test_plane),epsilon))
# print('N of plane',normal_vector_from_plane(p0,p1,p2))
# print('N of plane',normal_vector_from_plane(sa,sb,sq6))
# print("///square result=",is_inside_plane(sa, sb, sc, sd, sq6))
return all(np.round(tnormal_basic_plane,epsilon) == np.round(tnormal_test_plane,epsilon))
def check_available_point_on_plane(p0, p1, p3, p2, tpnt):
ret_inside = is_inside_plane(p0, p1, p3, p2, tpnt)
ret_on_plane = is_same_on_plane(p0, p1, p3, tpnt)
print(" ret inside=",ret_inside,", ret_on_plane", ret_on_plane)
print("final",all([ret_inside, ret_on_plane]))
return all([ret_inside, ret_on_plane])
if __name__=="__main__":
# # #Define plane
# # planeNormal = np.array([0, 0, 1])
# # planePoint = np.array([0, 0, 5]) #Any point on the plane
# #
# # #Define ray
# # rayDirection = np.array([0, -1, -1])
# # rayPoint = np.array([0, 0, 10]) #Any point along the ray
#
# #Define plane
# planeNormal = np.array([-0.51503999, 0, 0.85716615])
# planePoint = np.array([937.15, -350., 802.538]) #Any point on the plane
# # planePoint = np.array([1224.3, - 800., 975.076]) #Any point on the plane
#
# # at[383.70970791 - 456.45847575
# # 469.99584065]
#
# #Define ray
# # rayDirection = np.array([0.94451975, 0.02913004, 0.32716034])
# rayDirection = np.array([0.94451975, 0.02913004, 0.32716034])
# rayPoint = np.array([1501, -422, 857]) #Any point along the ray
#
# Psi = line_plane_collision(planeNormal, planePoint, rayDirection, rayPoint)
# print ("intersection at", Psi)
#
# result = lineIntersection(planeNormal, planePoint, rayDirection, rayPoint)
# print ("lineIntersection1 at", result)
#
# result = lineIntersection2(planeNormal, planePoint, rayDirection, rayPoint)
# print ("lineIntersection2 at", result)
#
# # print(*map(lambda x: np.array(*x), [(0, 0), (10, 10), (6, 2), (2, 2)]))
# # isInside(*map(lambda x: Vector(*x), [(0, 0), (10, 10), (6, 2), (2, 2)]))
# print('\n\n')
# a = np.array(( 0, 0, 0))
# b = np.array((10,10, 0))
# c = np.array(( 6, 2, 0))
# q = np.array(( 5, 3, 0)) # true
# q1 = np.array(( 8, 0, 0)) # false
# q2 = np.array((11,11, 0)) # false
# q3 = np.array(( 1,10, 0)) # false
# q4 = np.array((-10,10,0)) # false
# q5 = np.array(( 8, 6, 0)) # true
#
# # print(is_sameside_on_line(a, b, c, q3))
# print("///triangle result=",is_inside_triangle(a, b, c, q5))
#
# sa = np.array(( 0, 0, 0))
# sb = np.array((10, 0, 0))
# sc = np.array((10,10, 0))
# sd = np.array(( 0,10, 0))
# sq1 = np.array(( 1, 1, 0)) # true
# sq2 = np.array((11,11, 0)) # false
# sq3 = np.array(( 1,10, 0)) # ??겹침 true
# sq4 = np.array((-10,10,0)) # false
# sq5 = np.array(( 5,-1, 0)) # false
# sq6 = np.array(( 8, 4, 0)) # true
#
# print("///square result=",is_inside_plane(sa, sb, sc, sd, sq6))
# # print(1/0)
#
# print("\n\ndouble check.......")
# # p0 = top_left = np.array([1316, -127, 985])
# # p1 = top_right = np.array([1316, 127, 985])
# # p2 = bottom_left = np.array([1316, -127, 905])
# p0 = top_left = np.array([1224.3, -800, 975.076])
# p1 = top_right = np.array([1224.3, 100, 975.076])
# p2 = bottom_left = np.array([650, -800, 630])
# p3 = bottom_right = bottom_left + top_right - top_left
#
# tpnt = np.array([383.70970819, -456.45847574, 469.99584075]) #point of square from vector -Head Eye gaze [0.94451975 0.02913004 0.32716034]
# # -> user input unitvec2radian [ 0., -19.09650997, 1.76650551]
# tpnt2 = np.array([937.15, -350., 802.538]) #center of square
# tpnt3 = np.array([1065.46305, - 435.432, 706.13982]) #virtual point(from user)
# tpnt4 = np.array([1221.56363, 43.727, 973.43181]) #virtual point(from user)-Head Eye gaze(0.50306617 -0.83844362 -0.20961)]
# #-> user input unitvec2radian [-0. 12.09949823 - 59.03825349]
# tpnt5 = np.array([1002.18644251, -594.77776676, 841.61603489]) ##virtual point(from user2 swap(y,z))-Head Eye gaze [0.94451975, 0.32716034, 0.02913004 ]
#
# print("///square result=", is_inside_plane(p0, p1, p3, p2, tpnt))
#
# print(np.dot(planeNormal, planePoint))
# print(np.dot(planeNormal, p0))
# print(np.dot(planeNormal, p1))
# print(np.dot(planeNormal, p2))
# print(np.dot(planeNormal, p3))
# print(np.dot(planeNormal, tpnt))
# print(np.dot(planeNormal, tpnt2))
# print(np.dot(planeNormal, tpnt2))
#
# print(np.cross((p3 - p1), (p2 - p3)) / np.linalg.norm(np.cross((p3 - p1), (p2 - p3))))
# print(np.cross((p3 - p1), (p2 - p1)) / np.linalg.norm(np.cross((p3 - p1), (p2 - p1))))
# print(np.cross((p3 - p1), (p0 - p3)) / np.linalg.norm(np.cross((p3 - p1), (p0 - p3))))
# print(np.cross((p3 - p1), (tpnt2 - p3)) / np.linalg.norm(np.cross((p3 - p1), (tpnt2 - p3))))
#
# print(np.cross((p3 - p1), (p2 - p3)) )
# print(np.cross((p3 - p1), (p2 - p1)) )
# print(np.cross((p3 - p1), (p0 - p3)) )
# print(np.cross((p3 - p1), (tpnt2 - p3)) )
#
# print(np.cross((sb - sa), (sd - sa)) )
# print(np.dot((sb - sa), (sc - sa)))
#
#
# print('N of plane',normal_vector_from_plane(sa,sb,sc))
# print('N of plane',normal_vector_from_plane(sa,sb,sq6))
# print(is_same_on_plane(sa, sb, sc, sq6))
# print(is_same_on_plane(sa, sb, sc, np.array((8, 4, 1))))
# print(is_same_on_plane(p0, p1, p2, tpnt2))
# print(is_same_on_plane(p0, p1, p2, tpnt))
#
# check_available_point_on_plane(p0, p1, p3, p2, tpnt)
# check_available_point_on_plane(p0, p1, p3, p2, tpnt2)
# check_available_point_on_plane(sa, sb, sc, sd, np.array((8, 4, 1)))
# check_available_point_on_plane(sa, sb, sc, sd, sq6)
# check_available_point_on_plane(p0, p1, p3, p2, tpnt3)
# check_available_point_on_plane(p0, p1, p3, p2, tpnt4)
# check_available_point_on_plane(p0, p1, p3, p2, tpnt5)
#
# theta = 180 * deg2Rad
# print(theta)
# R_y = np.array([[math.cos(theta), 0, math.sin(theta)],
# [0, 1, 0],
# [-math.sin(theta), 0, math.cos(theta)]])
# R_z = np.array([[math.cos(theta), -math.sin(theta), 0],
# [math.sin(theta), math.cos(theta), 0],
# [0, 0, 1]])
# vvv = np.array([1,1,1])
# R = np.dot(R_y, vvv)
# R2 = np.dot(R_z, vvv)
#
# print('R',R)
# print('R2',R2)
#
# aaaaa = line_plane_collision(planeNormal, planePoint, np.array([0.94464068, 0.02371891, 0.32724823]), rayPoint)
# bbbbb = line_plane_collision(planeNormal, planePoint, np.array([0.99979601, -0.01828377, 0.00858109]), rayPoint)
# ccccc = line_plane_collision(planeNormal, planePoint, np.array([0.99938273, 0.03406657, 0.008581099]), rayPoint)
# ddddd = line_plane_collision(planeNormal, planePoint, np.array([-0.32626789, -0.0315359, 0.94475116]), rayPoint)
#
# print ("intersection at", aaaaa)
# print ("intersection at", bbbbb)
# print ("intersection at", ccccc)
# print ("intersection at", ddddd)
#
# # check_available_point_on_plane(p0, p1, p3, p2, aaaaa)
# # check_available_point_on_plane(p0, p1, p3, p2, bbbbb)
# check_available_point_on_plane(p0, p1, p3, p2, ccccc)
# # check_available_point_on_plane(p0, p1, p3, p2, ddddd)
# # print(1/0)
#
# # headOri_deg[1.5, - 9.3,1.5]
# # lpupil_deg[0., - 9.8 , 0.2]
# # print())
print(np.dot(eulerAnglesToRotationMatrix(np.array([0,0,math.pi])), np.array([1,1,1])).round(5))
a=np.array([1511, - 380, 860])
b=np.array([0.29828439, - 0.93999239, 0.16565246])
c=np.array([0., 1., 0.])
d=np.array([1551.94, 700., 437.87975])
bb= np.dot(eulerAnglesToRotationMatrix(np.array([0,0,math.pi])), b).round(5)
# tview_point[-1168.2874988, - 700., - 669.67435845]
ddddd = line_plane_collision(c, d, b, a)
print(ddddd)
# #같은 방향 유무 판별
print(np.dot((ddddd - a),bb))
print((ddddd - a), bb)
nor = (ddddd - a) / np.linalg.norm((ddddd - a))
print('nor',nor)
print('\n\n\n')
a2=np.array([1511, - 380, 860])
b2=np.array([0.29828439, - 0.93999239, 0.16565246])
c2=np.array([0., 1., 0.])
d2=np.array([1551.94, - 800, 437.87975])
bb2= np.dot(eulerAnglesToRotationMatrix(np.array([0,0,math.pi])), b2).round(5)
# tview_point[-1644.2770838, 800., - 934.01552727]
ddddd2 = line_plane_collision(c2, d2, b2, a2)
print(ddddd2)
print(np.dot((ddddd2 - a2),bb2))
print((ddddd2 - a2), bb2)
nor = (ddddd2 - a2) / np.linalg.norm((ddddd2 - a2))
print('nor',nor)
print('\n\n\n')
a3=np.array([1496, - 438, 860])
b3=np.array([0.97196993, 0.23393656, 0.0234124])
c3=np.array([-0.51503999, 0., 0.85716615])
d3=np.array([937.15, - 350., 802.538])
bb3 = np.dot(eulerAnglesToRotationMatrix(np.array([0, 0, math.pi])), b3).round(5)
# tview_point[-1013.43724481, 554.14461325, - 848.37623314]
# tview_point2[1013.43724481, - 554.14461325, 848.37623314]
ddddd3 = line_plane_collision(c3, d3, b3, a3)
print(ddddd3)
print(np.dot((ddddd3 - a3),bb3))
print((ddddd3 - a3), bb3)
nor = (ddddd3 - a3) / np.linalg.norm((ddddd3 - a3))
print('nor',nor)