让我们开始考虑两种类型的相机旋转：

摄像机绕点旋转（轨道）：

def rotate_around_target(self, target, delta):
    right = (self.target - self.eye).cross(self.up).normalize()
    amount = (right * delta.y + self.up * delta.x)
    self.target = target
    self.up = self.original_up
    self.eye = (
        mat4.rotatez(amount.z) *
        mat4.rotatey(amount.y) *
        mat4.rotatex(amount.x) *
        vec3(self.eye)
    )

相机旋转目标（FPS）

def rotate_target(self, delta):
    right = (self.target - self.eye).cross(self.up).normalize()
    self.target = (
        mat4.translate(self.eye) *
        mat4().rotate(delta.y, right) *
        mat4().rotate(delta.x, self.up) *
        mat4.translate(-self.eye) *
        self.target
    )

然后是一个更新函数，其中从眼睛/目标/上摄像机矢量中计算出投影/视图矩阵：

def update(self, aspect):
    self.view = mat4.lookat(self.eye, self.target, self.up)
    self.projection = mat4.perspective_fovx(
        self.fov, aspect, self.near, self.far
    )

当摄像机的视图方向与上轴平行（在此处为z-up）时，出现这些旋转功能的问题…在那时，摄像机的行为确实令人讨厌，因此我将遇到以下故障：

所以我的问题是，我该如何调整以上代码，使相机完整旋转，而最终结果在某些边缘点上看起来并不奇怪（相机轴围绕：/翻转）？

我希望具有与许多DCC程序包（3dsmax，maya等）相同的行为，在这些程序包中它们进行完整的旋转而不会出现任何奇怪的行为。

编辑：

对于那些想尝试一下数学的人，我决定创建一个非常简单的版本，该版本能够重现所解释的问题：

import math
from ctypes import c_void_p

import numpy as np
from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *

import glm


class Camera():

    def __init__(
        self,
        eye=None, target=None, up=None,
        fov=None, near=0.1, far=100000
    ):
        self.eye = eye or glm.vec3(0, 0, 1)
        self.target = target or glm.vec3(0, 0, 0)
        self.up = up or glm.vec3(0, 1, 0)
        self.original_up = glm.vec3(self.up)
        self.fov = fov or glm.radians(45)
        self.near = near
        self.far = far

    def update(self, aspect):
        self.view = glm.lookAt(
            self.eye, self.target, self.up
        )
        self.projection = glm.perspective(
            self.fov, aspect, self.near, self.far
        )

    def rotate_target(self, delta):
        right = glm.normalize(glm.cross(self.target - self.eye, self.up))
        M = glm.mat4(1)
        M = glm.translate(M, self.eye)
        M = glm.rotate(M, delta.y, right)
        M = glm.rotate(M, delta.x, self.up)
        M = glm.translate(M, -self.eye)
        self.target = glm.vec3(M * glm.vec4(self.target, 1.0))

    def rotate_around_target(self, target, delta):
        right = glm.normalize(glm.cross(self.target - self.eye, self.up))
        amount = (right * delta.y + self.up * delta.x)
        M = glm.mat4(1)
        M = glm.rotate(M, amount.z, glm.vec3(0, 0, 1))
        M = glm.rotate(M, amount.y, glm.vec3(0, 1, 0))
        M = glm.rotate(M, amount.x, glm.vec3(1, 0, 0))
        self.eye = glm.vec3(M * glm.vec4(self.eye, 1.0))
        self.target = target
        self.up = self.original_up

    def rotate_around_origin(self, delta):
        return self.rotate_around_target(glm.vec3(0), delta)


class GlutController():

    FPS = 0
    ORBIT = 1

    def __init__(self, camera, velocity=100, velocity_wheel=100):
        self.velocity = velocity
        self.velocity_wheel = velocity_wheel
        self.camera = camera

    def glut_mouse(self, button, state, x, y):
        self.mouse_last_pos = glm.vec2(x, y)
        self.mouse_down_pos = glm.vec2(x, y)

        if button == GLUT_LEFT_BUTTON:
            self.mode = self.FPS
        elif button == GLUT_RIGHT_BUTTON:
            self.mode = self.ORBIT

    def glut_motion(self, x, y):
        pos = glm.vec2(x, y)
        move = self.mouse_last_pos - pos
        self.mouse_last_pos = pos

        if self.mode == self.FPS:
            self.camera.rotate_target(move * 0.005)
        elif self.mode == self.ORBIT:
            self.camera.rotate_around_origin(move * 0.005)


class MyWindow:

    def __init__(self, w, h):
        self.width = w
        self.height = h

        glutInit()
        glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH)
        glutInitWindowSize(w, h)
        glutCreateWindow('OpenGL Window')

        self.startup()

        glutReshapeFunc(self.reshape)
        glutDisplayFunc(self.display)
        glutMouseFunc(self.controller.glut_mouse)
        glutMotionFunc(self.controller.glut_motion)
        glutIdleFunc(self.idle_func)

    def startup(self):
        glEnable(GL_DEPTH_TEST)

        aspect = self.width / self.height
        self.camera = Camera(
            eye=glm.vec3(10, 10, 10),
            target=glm.vec3(0, 0, 0),
            up=glm.vec3(0, 1, 0)
        )
        self.model = glm.mat4(1)
        self.controller = GlutController(self.camera)

    def run(self):
        glutMainLoop()

    def idle_func(self):
        glutPostRedisplay()

    def reshape(self, w, h):
        glViewport(0, 0, w, h)
        self.width = w
        self.height = h

    def display(self):
        self.camera.update(self.width / self.height)

        glClearColor(0.2, 0.3, 0.3, 1.0)
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

        glMatrixMode(GL_PROJECTION)
        glLoadIdentity()
        gluPerspective(glm.degrees(self.camera.fov), self.width / self.height, self.camera.near, self.camera.far)
        glMatrixMode(GL_MODELVIEW)
        glLoadIdentity()
        e = self.camera.eye
        t = self.camera.target
        u = self.camera.up
        gluLookAt(e.x, e.y, e.z, t.x, t.y, t.z, u.x, u.y, u.z)
        glColor3f(1, 1, 1)
        glBegin(GL_LINES)
        for i in range(-5, 6):
            if i == 0:
                continue
            glVertex3f(-5, 0, i)
            glVertex3f(5, 0, i)
            glVertex3f(i, 0, -5)
            glVertex3f(i, 0, 5)
        glEnd()

        glBegin(GL_LINES)
        glColor3f(1, 0, 0)
        glVertex3f(-5, 0, 0)
        glVertex3f(5, 0, 0)
        glColor3f(0, 1, 0)
        glVertex3f(0, -5, 0)
        glVertex3f(0, 5, 0)
        glColor3f(0, 0, 1)
        glVertex3f(0, 0, -5)
        glVertex3f(0, 0, 5)
        glEnd()

        glutSwapBuffers()


if __name__ == '__main__':
    window = MyWindow(800, 600)
    window.run()

为了运行它，您需要安装pyopengl和pyglm