如何在 PyOpenGL 中获取当前相机位置？

Question

我正在用 OpenGL 制作一个游戏，其中一些物体会朝向你。为此，我必须获取当前的相机位置。我知道在 OpenGL 中相机总是停留在 (0,0,0) 位置，但我想根据世界获取相机的当前位置。我该怎么做>

我试过viewMatrix = glGetFloatv(GL_MODELVIEW_MATRIX) camera_pos = viewMatrix[3]，但是我的相机有俯仰和偏航，而且当我这样做时位置总是会改变。我该如何解决这个问题？

import pygame
from pygame.locals import *

from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *

import math,random

while run:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False
        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_ESCAPE:
                run = False
            if event.key == pygame.K_p:
                paused = not paused
        if not paused:
            if event.type == pygame.MOUSEMOTION:
                mouseMove = [event.pos[i] - displayCenter[i] for i in range(2)]
                pygame.mouse.set_pos(displayCenter) 

    pygame.mouse.set_visible(False)
    if not paused:
        #Get keys
        keypress = pygame.key.get_pressed()

        #Init model view matrix
        glLoadIdentity()

        #------------------------View------------------------
        #Apply the look up and down (with 90° angle limit)
        if up_down_angle < -90:
            if mouseMove[1] > 0:
                up_down_angle += mouseMove[1]*0.1
        elif up_down_angle > 90:
            if mouseMove[1] < 0:
                up_down_angle += mouseMove[1]*0.1
        else:
            up_down_angle += mouseMove[1]*0.1
        glRotatef(up_down_angle, 1.0, 0.0, 0.0)

        #Init the view matrix
        glPushMatrix()
        glLoadIdentity()

        #Apply the movement 
        if keypress[pygame.K_w]:
            glTranslatef(0,0,0.1)
        if keypress[pygame.K_s]:
            glTranslatef(0,0,-0.1)
        if keypress[pygame.K_d]:
            glTranslatef(-0.1,0,0)
        if keypress[pygame.K_a]:
            glTranslatef(0.1,0,0)

        #Apply the look left and right
        glRotatef(mouseMove[0]*0.1, 0.0, 1.0, 0.0)
        #------------------------View------------------------






        #------------------------Draw------------------------
        #Multiply the current matrix by the new view matrix and store the final view matrix 
        glMultMatrixf(viewMatrix)
        viewMatrix = glGetFloatv(GL_MODELVIEW_MATRIX)
        camera_pos = viewMatrix[3] #Incorrect
        print(camera_pos) #print the output

        #Apply view matrix
        glPopMatrix()
        glMultMatrixf(viewMatrix)

        glLightfv(GL_LIGHT0, GL_POSITION, [1, -1, 1, 0])

        glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)

        glPushMatrix()

        glColor4f(0.2, 0.2, 0.5, 1)
        for person in persons:
            person.draw()

        ground.draw()
        glutSwapBuffers()
        glPopMatrix()
        #------------------------Draw------------------------

        pygame.display.flip()
        pygame.time.wait(10)

pygame.quit()

我希望当我进行视图旋转时，我的坐标不会移动，但是这样做时 camera_pos 的输出会发生变化。

Answer 1

视图矩阵从世界空间转换为视图空间。这意味着视图矩阵不是包含相机位置的矩阵。视图矩阵是inverse matrix，其中包含相机位置和方向。

写一个可以计算4x4矩阵逆矩阵的函数：

def InverseMat44(mat):
    m = [mat[i][j] for i in range(4) for j in range(4)]
    inv = [0]*16

    inv[0]  =  m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15] + m[9] * m[7] * m[14] + m[13] * m[6] * m[11] - m[13] * m[7] * m[10]
    inv[4]  = -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15] - m[8] * m[7] * m[14] - m[12] * m[6] * m[11] + m[12] * m[7] * m[10]
    inv[8]  =  m[4] * m[9]  * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15] + m[8] * m[7] * m[13] + m[12] * m[5] * m[11] - m[12] * m[7] * m[9]
    inv[12] = -m[4] * m[9]  * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14] - m[8] * m[6] * m[13] - m[12] * m[5] * m[10] + m[12] * m[6] * m[9]
    inv[1]  = -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15] - m[9] * m[3] * m[14] - m[13] * m[2] * m[11] + m[13] * m[3] * m[10]
    inv[5]  =  m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15] + m[8] * m[3] * m[14] + m[12] * m[2] * m[11] - m[12] * m[3] * m[10]
    inv[9]  = -m[0] * m[9]  * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15] - m[8] * m[3] * m[13] - m[12] * m[1] * m[11] + m[12] * m[3] * m[9]
    inv[13] =  m[0] * m[9]  * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14] + m[8] * m[2] * m[13] + m[12] * m[1] * m[10] - m[12] * m[2] * m[9]
    inv[2]  =  m[1] * m[6]  * m[15] - m[1] * m[7]  * m[14] - m[5] * m[2] * m[15] + m[5] * m[3] * m[14] + m[13] * m[2] * m[7]  - m[13] * m[3] * m[6]
    inv[6]  = -m[0] * m[6]  * m[15] + m[0] * m[7]  * m[14] + m[4] * m[2] * m[15] - m[4] * m[3] * m[14] - m[12] * m[2] * m[7]  + m[12] * m[3] * m[6]
    inv[10] =  m[0] * m[5]  * m[15] - m[0] * m[7]  * m[13] - m[4] * m[1] * m[15] + m[4] * m[3] * m[13] + m[12] * m[1] * m[7]  - m[12] * m[3] * m[5]
    inv[14] = -m[0] * m[5]  * m[14] + m[0] * m[6]  * m[13] + m[4] * m[1] * m[14] - m[4] * m[2] * m[13] - m[12] * m[1] * m[6]  + m[12] * m[2] * m[5]
    inv[3]  = -m[1] * m[6]  * m[11] + m[1] * m[7]  * m[10] + m[5] * m[2] * m[11] - m[5] * m[3] * m[10] - m[9]  * m[2] * m[7]  + m[9]  * m[3] * m[6]
    inv[7]  =  m[0] * m[6]  * m[11] - m[0] * m[7]  * m[10] - m[4] * m[2] * m[11] + m[4] * m[3] * m[10] + m[8]  * m[2] * m[7]  - m[8]  * m[3] * m[6]
    inv[11] = -m[0] * m[5]  * m[11] + m[0] * m[7]  * m[9]  + m[4] * m[1] * m[11] - m[4] * m[3] * m[9]  - m[8]  * m[1] * m[7]  + m[8]  * m[3] * m[5]
    inv[15] =  m[0] * m[5]  * m[10] - m[0] * m[6]  * m[9]  - m[4] * m[1] * m[10] + m[4] * m[2] * m[9]  + m[8]  * m[1] * m[6]  - m[8]  * m[2] * m[5]

    det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12]
    for i in range(16):
        inv[i] /= det;
    return inv;

另请参阅 inverting a 4x4 matrix 和 Find the inverse of a 4×4 matrix。

并计算视图矩阵的逆矩阵：

viewMatrix = glGetFloatv(GL_MODELVIEW_MATRIX)
invVM      = InverseMat44(viewMatrix)
camera_pos = (invVM[12], invVM[13], invVM[14])

print(camera_pos)

---

逆矩阵也可以通过库计算。例如numpy.linalg.inv 来自 NumPy 库或 glm.inverse 来自 PyGLM 库。