OPENGL glu透视实现
OPENGL gluPerspective implementation
我在实现自己的 gluPerspective 矩阵变换时遇到问题。它不显示任何内容。但是当我注释掉我的透视图实现时，使用 api，我的 Lookat 函数似乎可以工作。我不确定问题出在哪里？
这是我对矩阵变换的参考：
http://www.3dcpptutorials.sk/index.php?id=2
import sys, os
from math import pi as PI
from math import sin, cos
import math
from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *
import glfw
import numpy as np
def vec3(xx,yy,zz):
temp=[]
temp.append(xx)
temp.append(yy)
temp.append(zz)
return temp
def vec4(xx,yy,zz,dd):
temp=[]
temp.append(xx)
temp.append(yy)
temp.append(zz)
temp.append(dd)
return temp
########################################
class RenderWindow:
def __init__(self):
self.STEP2 = True
self.STEP3 = True
#########################################################
glfw.init()
self.width, self.height = 640, 480
self.win =glfw.create_window(self.width, self.height, "HW-SWGL-trans", None, None)
glfw.set_key_callback(self.win, self.on_key)
glfw.make_context_current(self.win)
glClearColor(0, 0, 0, 0)
glClearDepth(1.0)
glEnable(GL_DEPTH_TEST)
glDepthFunc(GL_LEQUAL)
self.exitNow = False
self.transformMat=np.identity(4)
self.ViewMat = np.identity(4)
self.ProjectionMat = np.identity(4)
self.winWidth = 1280
self.winHeight = 720
self.tho = 3.14159/4.0
self.theta = 3.14159/4.0
self.tetrahedron_verts=[]
for k in range(4):
self.tetrahedron_verts.append(vec3(0,0,0))
self.default_tetrahedron_vertices=[]
self.default_tetrahedron_vertices.append(vec3(1,0,0))
self.default_tetrahedron_vertices.append(vec3(0,1,0))
self.default_tetrahedron_vertices.append(vec3(0,0,1))
self.default_tetrahedron_vertices.append(vec3(0,0,0))
self.tetrahedron_verts=self.default_tetrahedron_vertices
def on_key(self, win, key, scancode, action, mods):
if action == glfw.PRESS:
if key == glfw.KEY_ESCAPE:
self.exitNow = True
if (key==glfw.KEY_Q):
glfw.set_window_title(self.win, "translate +x")
self.transformMat=np.matmul(self.swTranslate(1, 0, 0), self.transformMat)
if (key==glfw.KEY_A):
glfw.set_window_title(self.win, "translate -x")
self.transformMat=np.matmul(self.swTranslate(-1, 0, 0), self.transformMat)
if (key==glfw.KEY_W):
glfw.set_window_title(self.win, "translate +y")
self.transformMat=np.matmul(self.swTranslate(0, 1, 0), self.transformMat)
if (key==glfw.KEY_S):
glfw.set_window_title(self.win, "translate -y")
self.transformMat=np.matmul(self.swTranslate(0, -1, 0), self.transformMat)
if (key==glfw.KEY_E):
glfw.set_window_title(self.win, "translate +z")
self.transformMat=np.matmul(self.swTranslate(0, 0, 1), self.transformMat)
if (key==glfw.KEY_D):
glfw.set_window_title(self.win, "translate -z")
self.transformMat=np.matmul(self.swTranslate(0, 0, -1), self.transformMat)
if (key==glfw.KEY_R):
glfw.set_window_title(self.win, "rotate +x")
self.transformMat=np.matmul(self.swRotateX(self.tho), self.transformMat)
if (key==glfw.KEY_F):
glfw.set_window_title(self.win, "rotate -x")
self.transformMat=np.matmul(self.swRotateX(-self.tho), self.transformMat)
if (key==glfw.KEY_T):
glfw.set_window_title(self.win, "rotate +y")
self.transformMat=np.matmul(self.swRotateY(self.tho), self.transformMat)
if (key==glfw.KEY_G):
glfw.set_window_title(self.win, "rotate -y")
self.transformMat=np.matmul(self.swRotateY(-self.tho), self.transformMat)
if (key==glfw.KEY_Y):
glfw.set_window_title(self.win, "rotate +z")
self.transformMat=np.matmul(self.swRotateZ(self.tho), self.transformMat)
if (key==glfw.KEY_H):
glfw.set_window_title(self.win, "rotate -z")
self.transformMat=np.matmul(self.swRotateZ(-self.tho), self.transformMat)
if (key==glfw.KEY_U):
glfw.set_window_title(self.win, "scale +x")
self.transformMat=np.matmul(self.swScale(2,1,1), self.transformMat)
if (key==glfw.KEY_J):
glfw.set_window_title(self.win, "scale -x")
self.transformMat=np.matmul(self.swScale(1/2,1,1), self.transformMat)
if (key==glfw.KEY_I):
glfw.set_window_title(self.win, "scale +y")
self.transformMat=np.matmul(self.swScale(1,2,1), self.transformMat)
if (key==glfw.KEY_K):
glfw.set_window_title(self.win, "scale -y")
self.transformMat=np.matmul(self.swScale(1,1/2,1), self.transformMat)
if (key==glfw.KEY_O):
glfw.set_window_title(self.win, "scale +z")
self.transformMat=np.matmul(self.swScale(1,1,2), self.transformMat)
if (key==glfw.KEY_L):
glfw.set_window_title(self.win, "scale -z")
self.transformMat=np.matmul(self.swScale(1,1,1/2), self.transformMat)
#####################################################
if (key==glfw.KEY_F1): #you have to press fn and f1 at the same time
glfw.set_window_title(self.win, "F1: add a tetrahedron")
for i in range(4):
self.tetrahedron_verts[i] = self.default_tetrahedron_vertices[i]
if (key==glfw.KEY_F2):
glfw.set_window_title(self.win, "F2: add a cube or somthing")
if (key==glfw.KEY_F5):
glfw.set_window_title(self.win, "F5: SAVE")
if (key==glfw.KEY_F6):
glfw.set_window_title(self.win, "F6: LOAD")
if (key==glfw.KEY_9):
self.theta+=3.14159/90
if (key==glfw.KEY_0):
self.theta+=(-3.14159/90)
if (key==glfw.KEY_MINUS):
self.transformMat=np.identity(4)
def normal(self,vv):
norm=math.sqrt((vv[0])**2+(vv[1])**2+(vv[2])**2)
fin=np.true_divide(vv, norm)
return fin
def swScale(self,x,y,z):
Scale = np.identity(4)
Scale[0][0]=x
Scale[1][1]=y
Scale[2][2]=z
return Scale
def swRotate(self,angle,x,y,z):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)+pow(x,2)*(1-cos(angle))
Rotate[0][1]=x*y*(1-cos(angle))-z*sin(angle)
Rotate[0][2]=x*z*(1-cos(angle))+y*sin(angle)
Rotate[1][0]=y*x*(1-cos(angle))+z*sin(angle)
Rotate[1][1]=cos(angle)+pow(y,2)*(1-cos(angle))
Rotate[1][2]=y*z*(1-cos(angle))-x*sin(angle)
Rotate[2][0]=z*x*(1-cos(angle))-y*sin(angle)
Rotate[2][1]=z*y*(1-cos(angle))+x*sin(angle)
Rotate[2][2]=cos(angle)+pow(z,2)*(1-cos(angle))
return Rotate
def swRotateZ(self,angle):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)
Rotate[0][1]=-sin(angle)
Rotate[1][0]=sin(angle)
Rotate[1][1]=cos(angle)
return Rotate
def swRotateY(self,angle):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)
Rotate[0][2]=sin(angle)
Rotate[2][0]=-sin(angle)
Rotate[2][2]=cos(angle)
return Rotate
def swRotateX(self,angle):
Rotate = np.identity(4)
Rotate[1][1]=cos(angle)
Rotate[1][2]=-sin(angle)
Rotate[2][1]=sin(angle)
Rotate[2][2]=cos(angle)
return Rotate
def swTranslate(self,x,y,z):
Translate = np.identity(4)
#Translate[3][0] = x
#//todo: y z
Translate[0][3] = x
Translate[1][3] = y
Translate[2][3] = z
return Translate
def drawgrid(self):
size=10
glBegin(GL_LINES)
glColor3f(0.3, 0.3, 0.3)
for i in range(1,10):
self.drawp(i,-size,0)
self.drawp(i,size,0)
self.drawp(-i, -size, 0)
self.drawp(-i, size, 0)
self.drawp(-size, i, 0)
self.drawp(size, i, 0)
self.drawp(-size, -i, 0)
self.drawp(size, -i, 0)
glEnd()
glBegin(GL_LINES)
glColor3f(1, 0, 0)
self.drawp(0, 0, 0)
self.drawp(size, 0, 0)
glColor3f(0.4, 0, 0)
self.drawp(0, 0, 0)
self.drawp(-size, 0, 0)
glColor3f(0, 1, 0)
self.drawp(0, 0, 0)
self.drawp(0, size, 0)
glColor3f(0, 0.4, 0)
self.drawp(0, 0, 0)
self.drawp(0, -size, 0)
glColor3f(0, 0, 1)
self.drawp(0, 0, 0)
self.drawp(0, 0, size)
glEnd()
def drawp(self,p1,p2,p3):
#self.ProjectionMat
#np.array([p1, p2, p3, 1])
#self.ViewMat
tt=np.matmul(self.ProjectionMat,self.ViewMat)
tt=np.matmul(tt,np.array([p1, p2, p3, 1]))
glVertex3f(tt[0],tt[1],tt[2])
def Draw_Tetrahedron(self):
#vec3 color(1, 1, 0)
glColor3f(1, 1, 0)
glBegin(GL_TRIANGLES)
self.swTriangle(vec3(1, 0, 0), self.tetrahedron_verts[0], self.tetrahedron_verts[1], self.tetrahedron_verts[2], self.transformMat)
self.swTriangle(vec3(0, 0, 1), self.tetrahedron_verts[3], self.tetrahedron_verts[0], self.tetrahedron_verts[1], self.transformMat)
self.swTriangle(vec3(0, 1, 0), self.tetrahedron_verts[2], self.tetrahedron_verts[3], self.tetrahedron_verts[0], self.transformMat)
self.swTriangle(vec3(1, 1, 0), self.tetrahedron_verts[1], self.tetrahedron_verts[2], self.tetrahedron_verts[3], self.transformMat)
glEnd()
def swTriangle(self,color,in_v1,in_v2,in_v3,Modelmatrix):
v1=vec4(in_v1[0], in_v1[1], in_v1[2], 1)
v2=vec4(in_v2[0], in_v2[1], in_v2[2], 1)
v3=vec4(in_v3[0], in_v3[1], in_v3[2], 1)
##########################################
v1 = np.matmul(Modelmatrix,np.array(v1))
v2 = np.matmul(Modelmatrix,np.array(v2))
v3 = np.matmul(Modelmatrix,np.array(v3))
#step2: remove glLookAt, compute view matrix
v1 = np.matmul(self.ViewMat,v1)
v2 = np.matmul(self.ViewMat,v2)
v3 = np.matmul(self.ViewMat,v3)
#step3: remove glProjection, compute project matrix
#v1 = Projection * View * Modelmatrix * v1;
#prespective division
v1=np.matmul(self.ProjectionMat,v1)
v2=np.matmul(self.ProjectionMat,v2)
v3=np.matmul(self.ProjectionMat,v3)
##########################################
glColor3f(color[0], color[1], color[2])
glVertex3f(v1[0], v1[1], v1[2])
glVertex3f(v2[0], v2[1], v2[2])
glVertex3f(v3[0], v3[1], v3[2])
def swLookAt(self,eyex,eyey,eyez,atx,aty,atz,upx,upy,upz):
fx=atx-eyex
fy=aty-eyey
fz=atz-eyez
f=[]
f.append(fx)
f.append(fy)
f.append(fz)
f=np.array(f)
f=self.normal(f)
up=[]
up.append(upx)
up.append(upy)
up.append(upz)
up=np.array(up)
up=self.normal(up)
s=np.cross(f, up)
s=self.normal(s)
u=np.cross(s, f)
M=np.identity(4)
T=np.identity(4)
M[0][0]=s[0]
M[0][1]=s[1]
M[0][2]=s[2]
M[1][0]=u[0]
M[1][1]=u[1]
M[1][2]=u[2]
M[2][0]=-f[0]
M[2][1]=-f[1]
M[2][2]=-f[2]
T[0][3]=-eyex
T[1][3]=-eyey
T[2][3]=-eyez
mylookat=np.matmul(M,T)
return mylookat
def run(self):
t = 0.0
while not glfw.window_should_close(self.win) and not self.exitNow:
currT = GLUT.glutGet(GLUT_ELAPSED_TIME)
if currT - t > 0.1:
t = currT
self.display()
glfw.swap_buffers(self.win)
glfw.poll_events()
glfw.terminate()
def cot(self,x):
w1=sin(x)
w2=cos(x)
return (w2/w1)
def tan(self,x):
w1=sin(x)
w2=cos(x)
return (w1/w2)
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
#fovx=2*math.atan((aspect*self.tan(fovy/2)))
gg=(fovy/2)
#gg=math.radians(gg)
f=self.cot(gg)
per[0][0]=f/aspect
per[1][1]=f
per[2][2]=(near+far)/(near-far)
per[2][3]=(2*near*far)/(near-far)
per[3][2]=(-1)
return per
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
#glMatrixMode(GL_MODELVIEW)
#glLoadIdentity()
##gluLookAt(10*cos(self.theta), -10*sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
self.ViewMat=self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
if self.STEP3:
#glMatrixMode(GL_PROJECTION)
#glLoadIdentity()
#glOrtho(0, self.winWidth, 0, self.winHeight, -2.0, 2.0)
#gluPerspective(60, 1, 0.1, 50)
self.ProjectionMat=self.swPerspective(60, 1, 0.1, 50)
self.drawgrid()
self.Draw_Tetrahedron()
def main():
rw = RenderWindow()
rw.run()
if __name__ == "__main__":
main()
我认为问题应该出在以下函数上：
def drawp(self,p1,p2,p3):
#self.ProjectionMat
#np.array([p1, p2, p3, 1])
#self.ViewMat
tt=np.matmul(self.ProjectionMat,self.ViewMat)
tt=np.matmul(tt,np.array([p1, p2, p3, 1]))
glVertex3f(tt[0],tt[1],tt[2])
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
#fovx=2*math.atan((aspect*self.tan(fovy/2)))
gg=(fovy/2)
#gg=math.radians(gg)
f=self.cot(gg)
per[0][0]=f/aspect
per[1][1]=f
per[2][2]=(near+far)/(near-far)
per[2][3]=(2*near*far)/(near-far)
per[3][2]=(-1)
return per
要测试我的代码，只需注释掉 display() 中的 swPerspective 函数，使用 api。它会起作用。:
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
#glMatrixMode(GL_MODELVIEW)
#glLoadIdentity()
#gluLookAt(10*cos(self.theta), -10*sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
self.ViewMat=self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
if self.STEP3:
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
#glOrtho(0, self.winWidth, 0, self.winHeight, -2.0, 2.0)
gluPerspective(60, 1, 0.1, 50)
#self.ProjectionMat=self.swPerspective(60, 1, 0.1, 50)
self.drawgrid()
self.Draw_Tetrahedron()
投影矩阵和视图矩阵计算错误。 OpenGL 矩阵是列主序矩阵。因此，您需要转置矩阵。对于数学函数，角度的单位是弧度。但是，您的投影矩阵还有一些其他问题。参见 OpenGL Projection Matrix。正确的矩阵如下所示：
def swLookAt(self,eyex,eyey,eyez,atx,aty,atz,upx,upy,upz):
# [...]
mylookat=np.matmul(M,T).transpose()
return mylookat
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
f = math.tan(math.radians(fovy)/2)
per[0][0]= 1 / (f*aspect)
per[1][1]= 1 / f
per[2][2]=-(near+far)/(near-far)
per[3][2]=-(2*near*far)/(near-far)
per[2][3]=(-1)
return per
此外，您必须使用 glLoadMatrixf:
加载矩阵
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
glMatrixMode(GL_MODELVIEW)
glLoadMatrixf(self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1))
if self.STEP3:
glMatrixMode(GL_PROJECTION)
glLoadMatrixf(self.swPerspective(60, 1, 0.1, 50))
self.drawgrid()
self.Draw_Tetrahedron()
我在实现自己的 gluPerspective 矩阵变换时遇到问题。它不显示任何内容。但是当我注释掉我的透视图实现时，使用 api，我的 Lookat 函数似乎可以工作。我不确定问题出在哪里？ 这是我对矩阵变换的参考： http://www.3dcpptutorials.sk/index.php?id=2
import sys, os
from math import pi as PI
from math import sin, cos
import math
from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *
import glfw
import numpy as np
def vec3(xx,yy,zz):
temp=[]
temp.append(xx)
temp.append(yy)
temp.append(zz)
return temp
def vec4(xx,yy,zz,dd):
temp=[]
temp.append(xx)
temp.append(yy)
temp.append(zz)
temp.append(dd)
return temp
########################################
class RenderWindow:
def __init__(self):
self.STEP2 = True
self.STEP3 = True
#########################################################
glfw.init()
self.width, self.height = 640, 480
self.win =glfw.create_window(self.width, self.height, "HW-SWGL-trans", None, None)
glfw.set_key_callback(self.win, self.on_key)
glfw.make_context_current(self.win)
glClearColor(0, 0, 0, 0)
glClearDepth(1.0)
glEnable(GL_DEPTH_TEST)
glDepthFunc(GL_LEQUAL)
self.exitNow = False
self.transformMat=np.identity(4)
self.ViewMat = np.identity(4)
self.ProjectionMat = np.identity(4)
self.winWidth = 1280
self.winHeight = 720
self.tho = 3.14159/4.0
self.theta = 3.14159/4.0
self.tetrahedron_verts=[]
for k in range(4):
self.tetrahedron_verts.append(vec3(0,0,0))
self.default_tetrahedron_vertices=[]
self.default_tetrahedron_vertices.append(vec3(1,0,0))
self.default_tetrahedron_vertices.append(vec3(0,1,0))
self.default_tetrahedron_vertices.append(vec3(0,0,1))
self.default_tetrahedron_vertices.append(vec3(0,0,0))
self.tetrahedron_verts=self.default_tetrahedron_vertices
def on_key(self, win, key, scancode, action, mods):
if action == glfw.PRESS:
if key == glfw.KEY_ESCAPE:
self.exitNow = True
if (key==glfw.KEY_Q):
glfw.set_window_title(self.win, "translate +x")
self.transformMat=np.matmul(self.swTranslate(1, 0, 0), self.transformMat)
if (key==glfw.KEY_A):
glfw.set_window_title(self.win, "translate -x")
self.transformMat=np.matmul(self.swTranslate(-1, 0, 0), self.transformMat)
if (key==glfw.KEY_W):
glfw.set_window_title(self.win, "translate +y")
self.transformMat=np.matmul(self.swTranslate(0, 1, 0), self.transformMat)
if (key==glfw.KEY_S):
glfw.set_window_title(self.win, "translate -y")
self.transformMat=np.matmul(self.swTranslate(0, -1, 0), self.transformMat)
if (key==glfw.KEY_E):
glfw.set_window_title(self.win, "translate +z")
self.transformMat=np.matmul(self.swTranslate(0, 0, 1), self.transformMat)
if (key==glfw.KEY_D):
glfw.set_window_title(self.win, "translate -z")
self.transformMat=np.matmul(self.swTranslate(0, 0, -1), self.transformMat)
if (key==glfw.KEY_R):
glfw.set_window_title(self.win, "rotate +x")
self.transformMat=np.matmul(self.swRotateX(self.tho), self.transformMat)
if (key==glfw.KEY_F):
glfw.set_window_title(self.win, "rotate -x")
self.transformMat=np.matmul(self.swRotateX(-self.tho), self.transformMat)
if (key==glfw.KEY_T):
glfw.set_window_title(self.win, "rotate +y")
self.transformMat=np.matmul(self.swRotateY(self.tho), self.transformMat)
if (key==glfw.KEY_G):
glfw.set_window_title(self.win, "rotate -y")
self.transformMat=np.matmul(self.swRotateY(-self.tho), self.transformMat)
if (key==glfw.KEY_Y):
glfw.set_window_title(self.win, "rotate +z")
self.transformMat=np.matmul(self.swRotateZ(self.tho), self.transformMat)
if (key==glfw.KEY_H):
glfw.set_window_title(self.win, "rotate -z")
self.transformMat=np.matmul(self.swRotateZ(-self.tho), self.transformMat)
if (key==glfw.KEY_U):
glfw.set_window_title(self.win, "scale +x")
self.transformMat=np.matmul(self.swScale(2,1,1), self.transformMat)
if (key==glfw.KEY_J):
glfw.set_window_title(self.win, "scale -x")
self.transformMat=np.matmul(self.swScale(1/2,1,1), self.transformMat)
if (key==glfw.KEY_I):
glfw.set_window_title(self.win, "scale +y")
self.transformMat=np.matmul(self.swScale(1,2,1), self.transformMat)
if (key==glfw.KEY_K):
glfw.set_window_title(self.win, "scale -y")
self.transformMat=np.matmul(self.swScale(1,1/2,1), self.transformMat)
if (key==glfw.KEY_O):
glfw.set_window_title(self.win, "scale +z")
self.transformMat=np.matmul(self.swScale(1,1,2), self.transformMat)
if (key==glfw.KEY_L):
glfw.set_window_title(self.win, "scale -z")
self.transformMat=np.matmul(self.swScale(1,1,1/2), self.transformMat)
#####################################################
if (key==glfw.KEY_F1): #you have to press fn and f1 at the same time
glfw.set_window_title(self.win, "F1: add a tetrahedron")
for i in range(4):
self.tetrahedron_verts[i] = self.default_tetrahedron_vertices[i]
if (key==glfw.KEY_F2):
glfw.set_window_title(self.win, "F2: add a cube or somthing")
if (key==glfw.KEY_F5):
glfw.set_window_title(self.win, "F5: SAVE")
if (key==glfw.KEY_F6):
glfw.set_window_title(self.win, "F6: LOAD")
if (key==glfw.KEY_9):
self.theta+=3.14159/90
if (key==glfw.KEY_0):
self.theta+=(-3.14159/90)
if (key==glfw.KEY_MINUS):
self.transformMat=np.identity(4)
def normal(self,vv):
norm=math.sqrt((vv[0])**2+(vv[1])**2+(vv[2])**2)
fin=np.true_divide(vv, norm)
return fin
def swScale(self,x,y,z):
Scale = np.identity(4)
Scale[0][0]=x
Scale[1][1]=y
Scale[2][2]=z
return Scale
def swRotate(self,angle,x,y,z):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)+pow(x,2)*(1-cos(angle))
Rotate[0][1]=x*y*(1-cos(angle))-z*sin(angle)
Rotate[0][2]=x*z*(1-cos(angle))+y*sin(angle)
Rotate[1][0]=y*x*(1-cos(angle))+z*sin(angle)
Rotate[1][1]=cos(angle)+pow(y,2)*(1-cos(angle))
Rotate[1][2]=y*z*(1-cos(angle))-x*sin(angle)
Rotate[2][0]=z*x*(1-cos(angle))-y*sin(angle)
Rotate[2][1]=z*y*(1-cos(angle))+x*sin(angle)
Rotate[2][2]=cos(angle)+pow(z,2)*(1-cos(angle))
return Rotate
def swRotateZ(self,angle):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)
Rotate[0][1]=-sin(angle)
Rotate[1][0]=sin(angle)
Rotate[1][1]=cos(angle)
return Rotate
def swRotateY(self,angle):
Rotate = np.identity(4)
Rotate[0][0]=cos(angle)
Rotate[0][2]=sin(angle)
Rotate[2][0]=-sin(angle)
Rotate[2][2]=cos(angle)
return Rotate
def swRotateX(self,angle):
Rotate = np.identity(4)
Rotate[1][1]=cos(angle)
Rotate[1][2]=-sin(angle)
Rotate[2][1]=sin(angle)
Rotate[2][2]=cos(angle)
return Rotate
def swTranslate(self,x,y,z):
Translate = np.identity(4)
#Translate[3][0] = x
#//todo: y z
Translate[0][3] = x
Translate[1][3] = y
Translate[2][3] = z
return Translate
def drawgrid(self):
size=10
glBegin(GL_LINES)
glColor3f(0.3, 0.3, 0.3)
for i in range(1,10):
self.drawp(i,-size,0)
self.drawp(i,size,0)
self.drawp(-i, -size, 0)
self.drawp(-i, size, 0)
self.drawp(-size, i, 0)
self.drawp(size, i, 0)
self.drawp(-size, -i, 0)
self.drawp(size, -i, 0)
glEnd()
glBegin(GL_LINES)
glColor3f(1, 0, 0)
self.drawp(0, 0, 0)
self.drawp(size, 0, 0)
glColor3f(0.4, 0, 0)
self.drawp(0, 0, 0)
self.drawp(-size, 0, 0)
glColor3f(0, 1, 0)
self.drawp(0, 0, 0)
self.drawp(0, size, 0)
glColor3f(0, 0.4, 0)
self.drawp(0, 0, 0)
self.drawp(0, -size, 0)
glColor3f(0, 0, 1)
self.drawp(0, 0, 0)
self.drawp(0, 0, size)
glEnd()
def drawp(self,p1,p2,p3):
#self.ProjectionMat
#np.array([p1, p2, p3, 1])
#self.ViewMat
tt=np.matmul(self.ProjectionMat,self.ViewMat)
tt=np.matmul(tt,np.array([p1, p2, p3, 1]))
glVertex3f(tt[0],tt[1],tt[2])
def Draw_Tetrahedron(self):
#vec3 color(1, 1, 0)
glColor3f(1, 1, 0)
glBegin(GL_TRIANGLES)
self.swTriangle(vec3(1, 0, 0), self.tetrahedron_verts[0], self.tetrahedron_verts[1], self.tetrahedron_verts[2], self.transformMat)
self.swTriangle(vec3(0, 0, 1), self.tetrahedron_verts[3], self.tetrahedron_verts[0], self.tetrahedron_verts[1], self.transformMat)
self.swTriangle(vec3(0, 1, 0), self.tetrahedron_verts[2], self.tetrahedron_verts[3], self.tetrahedron_verts[0], self.transformMat)
self.swTriangle(vec3(1, 1, 0), self.tetrahedron_verts[1], self.tetrahedron_verts[2], self.tetrahedron_verts[3], self.transformMat)
glEnd()
def swTriangle(self,color,in_v1,in_v2,in_v3,Modelmatrix):
v1=vec4(in_v1[0], in_v1[1], in_v1[2], 1)
v2=vec4(in_v2[0], in_v2[1], in_v2[2], 1)
v3=vec4(in_v3[0], in_v3[1], in_v3[2], 1)
##########################################
v1 = np.matmul(Modelmatrix,np.array(v1))
v2 = np.matmul(Modelmatrix,np.array(v2))
v3 = np.matmul(Modelmatrix,np.array(v3))
#step2: remove glLookAt, compute view matrix
v1 = np.matmul(self.ViewMat,v1)
v2 = np.matmul(self.ViewMat,v2)
v3 = np.matmul(self.ViewMat,v3)
#step3: remove glProjection, compute project matrix
#v1 = Projection * View * Modelmatrix * v1;
#prespective division
v1=np.matmul(self.ProjectionMat,v1)
v2=np.matmul(self.ProjectionMat,v2)
v3=np.matmul(self.ProjectionMat,v3)
##########################################
glColor3f(color[0], color[1], color[2])
glVertex3f(v1[0], v1[1], v1[2])
glVertex3f(v2[0], v2[1], v2[2])
glVertex3f(v3[0], v3[1], v3[2])
def swLookAt(self,eyex,eyey,eyez,atx,aty,atz,upx,upy,upz):
fx=atx-eyex
fy=aty-eyey
fz=atz-eyez
f=[]
f.append(fx)
f.append(fy)
f.append(fz)
f=np.array(f)
f=self.normal(f)
up=[]
up.append(upx)
up.append(upy)
up.append(upz)
up=np.array(up)
up=self.normal(up)
s=np.cross(f, up)
s=self.normal(s)
u=np.cross(s, f)
M=np.identity(4)
T=np.identity(4)
M[0][0]=s[0]
M[0][1]=s[1]
M[0][2]=s[2]
M[1][0]=u[0]
M[1][1]=u[1]
M[1][2]=u[2]
M[2][0]=-f[0]
M[2][1]=-f[1]
M[2][2]=-f[2]
T[0][3]=-eyex
T[1][3]=-eyey
T[2][3]=-eyez
mylookat=np.matmul(M,T)
return mylookat
def run(self):
t = 0.0
while not glfw.window_should_close(self.win) and not self.exitNow:
currT = GLUT.glutGet(GLUT_ELAPSED_TIME)
if currT - t > 0.1:
t = currT
self.display()
glfw.swap_buffers(self.win)
glfw.poll_events()
glfw.terminate()
def cot(self,x):
w1=sin(x)
w2=cos(x)
return (w2/w1)
def tan(self,x):
w1=sin(x)
w2=cos(x)
return (w1/w2)
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
#fovx=2*math.atan((aspect*self.tan(fovy/2)))
gg=(fovy/2)
#gg=math.radians(gg)
f=self.cot(gg)
per[0][0]=f/aspect
per[1][1]=f
per[2][2]=(near+far)/(near-far)
per[2][3]=(2*near*far)/(near-far)
per[3][2]=(-1)
return per
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
#glMatrixMode(GL_MODELVIEW)
#glLoadIdentity()
##gluLookAt(10*cos(self.theta), -10*sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
self.ViewMat=self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
if self.STEP3:
#glMatrixMode(GL_PROJECTION)
#glLoadIdentity()
#glOrtho(0, self.winWidth, 0, self.winHeight, -2.0, 2.0)
#gluPerspective(60, 1, 0.1, 50)
self.ProjectionMat=self.swPerspective(60, 1, 0.1, 50)
self.drawgrid()
self.Draw_Tetrahedron()
def main():
rw = RenderWindow()
rw.run()
if __name__ == "__main__":
main()
我认为问题应该出在以下函数上：
def drawp(self,p1,p2,p3):
#self.ProjectionMat
#np.array([p1, p2, p3, 1])
#self.ViewMat
tt=np.matmul(self.ProjectionMat,self.ViewMat)
tt=np.matmul(tt,np.array([p1, p2, p3, 1]))
glVertex3f(tt[0],tt[1],tt[2])
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
#fovx=2*math.atan((aspect*self.tan(fovy/2)))
gg=(fovy/2)
#gg=math.radians(gg)
f=self.cot(gg)
per[0][0]=f/aspect
per[1][1]=f
per[2][2]=(near+far)/(near-far)
per[2][3]=(2*near*far)/(near-far)
per[3][2]=(-1)
return per
要测试我的代码，只需注释掉 display() 中的 swPerspective 函数，使用 api。它会起作用。:
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
#glMatrixMode(GL_MODELVIEW)
#glLoadIdentity()
#gluLookAt(10*cos(self.theta), -10*sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
self.ViewMat=self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1)
if self.STEP3:
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
#glOrtho(0, self.winWidth, 0, self.winHeight, -2.0, 2.0)
gluPerspective(60, 1, 0.1, 50)
#self.ProjectionMat=self.swPerspective(60, 1, 0.1, 50)
self.drawgrid()
self.Draw_Tetrahedron()
投影矩阵和视图矩阵计算错误。 OpenGL 矩阵是列主序矩阵。因此，您需要转置矩阵。对于数学函数，角度的单位是弧度。但是，您的投影矩阵还有一些其他问题。参见 OpenGL Projection Matrix。正确的矩阵如下所示：
def swLookAt(self,eyex,eyey,eyez,atx,aty,atz,upx,upy,upz):
# [...]
mylookat=np.matmul(M,T).transpose()
return mylookat
def swPerspective(self,fovy,aspect,near,far):
per=np.zeros((4,4))
f = math.tan(math.radians(fovy)/2)
per[0][0]= 1 / (f*aspect)
per[1][1]= 1 / f
per[2][2]=-(near+far)/(near-far)
per[3][2]=-(2*near*far)/(near-far)
per[2][3]=(-1)
return per
此外，您必须使用 glLoadMatrixf:
def display(self):
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
if self.STEP2:
glMatrixMode(GL_MODELVIEW)
glLoadMatrixf(self.swLookAt(10 * cos(self.theta), -10 * sin(self.theta), 10, 0, 0, 0, 0, 0, 1))
if self.STEP3:
glMatrixMode(GL_PROJECTION)
glLoadMatrixf(self.swPerspective(60, 1, 0.1, 50))
self.drawgrid()
self.Draw_Tetrahedron()