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关于python：处理相机旋转的正确方法

• python

Proper way to handle camera rotations

让我们从考虑 2 种类型的摄像机旋转开始：

相机围绕一个点旋转(Rails)：

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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)

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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
    )

然后只是一个更新函数，其中投影/视图矩阵是从眼睛/目标/向上相机向量中计算出来的：

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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
    )

当相机视图方向平行于上轴(此处为 z-up)时，这些旋转函数会出现问题……此时相机的行为非常糟糕，所以我会遇到诸如:

showcase

所以我的问题是，我怎样才能调整上面的代码，以便相机进行完整旋转，而最终结果在某些边缘点看起来很奇怪(相机轴翻转：/)？

我希望拥有与许多 DCC 软件包(3dsmax、maya、…)相同的行为，它们可以完全旋转而不会出现任何奇怪的行为。

编辑：

对于那些想试一试数学的人，我决定创建一个能够重现已解释问题的真正简约版本：

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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，你需要安装 pyopengl 和 pyglm

我建议在视图空间中绕轴旋转

你必须知道视图矩阵(V)。由于视图矩阵在 self.eye、self.target 和 self.up 中编码，因此必须通过 lookAt 计算：

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V = glm.lookAt(self.eye, self.target, self.up)

计算视图空间中的pivot，旋转angular和旋转轴。在这种情况下，轴是右旋转方向，其中 y 轴必须翻转：

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pivot = glm.vec3(V * glm.vec4(target.x, target.y, target.z, 1))
axis  = glm.vec3(-delta.y, -delta.x, 0)
angle = glm.length(delta)

设置旋转矩阵R并计算围绕枢轴RP的比率矩阵。最后通过旋转矩阵变换视图矩阵(V)。结果是新的视图矩阵 NV:

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R  = glm.rotate( glm.mat4(1), angle, axis )
RP = glm.translate(glm.mat4(1), pivot) * R * glm.translate(glm.mat4(1), -pivot)
NV = RP * V

从新的视图矩阵NV中解码self.eye、self.target和self.up：

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C = glm.inverse(NV)
targetDist  = glm.length(self.target – self.eye)
self.eye    = glm.vec3(C[3])
self.target = self.eye – glm.vec3(C[2]) * targetDist
self.up     = glm.vec3(C[1])

方法的完整编码 rotate_around_target_view:

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def rotate_around_target_view(self, target, delta):

    V = glm.lookAt(self.eye, self.target, self.up)

    pivot = glm.vec3(V * glm.vec4(target.x, target.y, target.z, 1))
    axis  = glm.vec3(-delta.y, -delta.x, 0)
    angle = glm.length(delta)

    R  = glm.rotate( glm.mat4(1), angle, axis )
    RP = glm.translate(glm.mat4(1), pivot) * R * glm.translate(glm.mat4(1), -pivot)
    NV = RP * V

    C = glm.inverse(NV)
    targetDist  = glm.length(self.target – self.eye)
    self.eye    = glm.vec3(C[3])
    self.target = self.eye – glm.vec3(C[2]) * targetDist
    self.up     = glm.vec3(C[1])

最后它可以围绕世界的原点和眼睛的位置甚至任何其他点进行旋转。

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

def rotate_target(self, delta):
    return self.rotate_around_target_view(self.eye, delta)

或者，可以在模型的世界空间中执行旋转。解决方案非常相似。
旋转是在世界空间中完成的，因此枢轴不必转换到视图空间，并且旋转应用于视图矩阵(NV = V * RP)之前：

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def rotate_around_target_world(self, target, delta):

    V = glm.lookAt(self.eye, self.target, self.up)

    pivot = target
    axis  = glm.vec3(-delta.y, -delta.x, 0)
    angle = glm.length(delta)

    R  = glm.rotate( glm.mat4(1), angle, axis )
    RP = glm.translate(glm.mat4(1), pivot) * R * glm.translate(glm.mat4(1), -pivot)
    NV = V * RP

    C = glm.inverse(NV)
    targetDist  = glm.length(self.target – self.eye)
    self.eye    = glm.vec3(C[3])
    self.target = self.eye – glm.vec3(C[2]) * targetDist
    self.up     = glm.vec3(C[1])

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

关于python：处理相机旋转的正确方法

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def rotate_around_target(self, target, delta):
    if abs(delta.x) > 0:
        self.rotate_around_target_world(target, glm.vec3(delta.x, 0.0, 0.0))
    if abs(delta.y) > 0:    
        self.rotate_around_target_view(target, glm.vec3(0.0, delta.y, 0.0))

我为了实现微创的方法，考虑到问题的原始代码，我会提出以下建议：

  • 操作后视图的目标应该是函数rotate_around_target的输入参数target。

  • 水平鼠标移动应该围绕世界的向上矢量旋转视图

  • 鼠标垂直移动应该围绕当前水平轴倾斜视图

我想出了以下方法：

  • 计算当前视线(los)、上向量(up)和水平轴(right)

  • 通过将上向量投影到由原始上向量和当前视线给定的平面上，使上向量垂直。这是通过 Gram-Schmidt 正交化实现的。

  • 围绕当前水平轴倾斜。这意味着 los 和 up 围绕 right 轴旋转。

  • 围绕向上矢量旋转。 los 和 right 围绕 up 旋转。

  • Calculate 设置并计算眼睛和目标位置，其中目标由输入参数target设置：

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    def rotate_around_target(self, target, delta):

        # get directions
        los    = self.target – self.eye
        losLen = glm.length(los)
        right  = glm.normalize(glm.cross(los, self.up))
        up     = glm.cross(right, los)

        # upright up vector (Gram–Schmidt orthogonalization)
        fix_right = glm.normalize(glm.cross(los, self.original_up))
        UPdotX    = glm.dot(fix_right, up)
        up        = glm.normalize(up – UPdotX * fix_right)
        right     = glm.normalize(glm.cross(los, up))
        los       = glm.cross(up, right)

        # tilt around horizontal axis
        RHor = glm.rotate(glm.mat4(1), delta.y, right)
        up   = glm.vec3(RHor * glm.vec4(up, 0.0))
        los  = glm.vec3(RHor * glm.vec4(los, 0.0))

        # rotate around up vector
        RUp   = glm.rotate(glm.mat4(1), delta.x, up)
        right = glm.vec3(RUp * glm.vec4(right, 0.0))
        los   = glm.vec3(RUp * glm.vec4(los, 0.0))

        # set eye, target and up
        self.eye    = target – los * losLen
        self.target = target
        self.up     = up

    以下是该线程中提供的所有答案的小总结：

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    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 zoom(self, *args):
            delta = -args[1] * 0.1
            distance = glm.length(self.target – self.eye)
            self.eye = self.target + (self.eye – self.target) * (delta + 1)

        def load_projection(self):
            width = glutGet(GLUT_WINDOW_WIDTH)
            height = glutGet(GLUT_WINDOW_HEIGHT)

            glMatrixMode(GL_PROJECTION)
            glLoadIdentity()
            gluPerspective(glm.degrees(self.fov), width / height, self.near, self.far)

        def load_modelview(self):
            e = self.eye
            t = self.target
            u = self.up

            glMatrixMode(GL_MODELVIEW)
            glLoadIdentity()
            gluLookAt(e.x, e.y, e.z, t.x, t.y, t.z, u.x, u.y, u.z)

    class CameraSkatic(Camera):

        def rotate_around_target(self, target, delta):
            M = glm.mat4(1)
            M = glm.rotate(M, delta.x, glm.vec3(0, 1, 0))
            M = glm.rotate(M, delta.y, glm.vec3(1, 0, 0))

            self.target = target
            T = glm.vec3(0, 0, glm.distance(self.target, self.eye))
            T = glm.vec3(M * glm.vec4(T, 0.0))
            self.eye = self.target + T
            self.up = glm.vec3(M * glm.vec4(self.original_up, 1.0))

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

    class CameraBPL(Camera):

        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 CameraRabbid76_v1(Camera):

        def rotate_around_target_world(self, target, delta):
            V = glm.lookAt(self.eye, self.target, self.up)

            pivot = target
            axis = glm.vec3(-delta.y, -delta.x, 0)
            angle = glm.length(delta)

            R = glm.rotate(glm.mat4(1), angle, axis)
            RP = glm.translate(glm.mat4(1), pivot) * R * glm.translate(glm.mat4(1), -pivot)
            NV = V * RP

            C = glm.inverse(NV)
            targetDist = glm.length(self.target – self.eye)
            self.eye = glm.vec3(C[3])
            self.target = self.eye – glm.vec3(C[2]) * targetDist
            self.up = glm.vec3(C[1])

        def rotate_around_target_view(self, target, delta):
            V = glm.lookAt(self.eye, self.target, self.up)

            pivot = glm.vec3(V * glm.vec4(target.x, target.y, target.z, 1))
            axis = glm.vec3(-delta.y, -delta.x, 0)
            angle = glm.length(delta)

            R = glm.rotate(glm.mat4(1), angle, axis)
            RP = glm.translate(glm.mat4(1), pivot) * R * glm.translate(glm.mat4(1), -pivot)
            NV = RP * V

            C = glm.inverse(NV)
            targetDist = glm.length(self.target – self.eye)
            self.eye = glm.vec3(C[3])
            self.target = self.eye – glm.vec3(C[2]) * targetDist
            self.up = glm.vec3(C[1])

        def rotate_around_target(self, target, delta):
            if abs(delta.x) > 0:
                self.rotate_around_target_world(target, glm.vec3(delta.x, 0.0, 0.0))
            if abs(delta.y) > 0:
                self.rotate_around_target_view(target, glm.vec3(0.0, delta.y, 0.0))

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

        def rotate_target(self, delta):
            return self.rotate_around_target(self.eye, delta)

    class CameraRabbid76_v2(Camera):

        def rotate_around_target(self, target, delta):

            # get directions
            los = self.target – self.eye
            losLen = glm.length(los)
            right = glm.normalize(glm.cross(los, self.up))
            up = glm.cross(right, los)

            # upright up vector (Gram–Schmidt orthogonalization)
            fix_right = glm.normalize(glm.cross(los, self.original_up))
            UPdotX = glm.dot(fix_right, up)
            up = glm.normalize(up – UPdotX * fix_right)
            right = glm.normalize(glm.cross(los, up))
            los = glm.cross(up, right)

            # tilt around horizontal axis
            RHor = glm.rotate(glm.mat4(1), delta.y, right)
            up = glm.vec3(RHor * glm.vec4(up, 0.0))
            los = glm.vec3(RHor * glm.vec4(los, 0.0))

            # rotate around up vector
            RUp = glm.rotate(glm.mat4(1), delta.x, up)
            right = glm.vec3(RUp * glm.vec4(right, 0.0))
            los = glm.vec3(RUp * glm.vec4(los, 0.0))

            # set eye, target and up
            self.eye = target – los * losLen
            self.target = target
            self.up = up

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

        def rotate_target(self, delta):
            return self.rotate_around_target(self.eye, 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)

        def glut_mouse_wheel(self, *args):
            self.camera.zoom(*args)

    def render_text(x, y, text):
        glColor3f(1, 1, 1)
        glRasterPos2f(x, y)
        glutBitmapString(GLUT_BITMAP_TIMES_ROMAN_24, text.encode("utf-8"))

    def draw_plane_yup():
        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, 1, 1)
        glVertex3f(–5, 0, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(0, 0, –5)
        glVertex3f(0, 0, 0)

        glColor3f(1, 0, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(5, 0, 0)
        glColor3f(0, 1, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(0, 5, 0)
        glColor3f(0, 0, 1)
        glVertex3f(0, 0, 0)
        glVertex3f(0, 0, 5)
        glEnd()

    def draw_plane_zup():
        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, –5, 0)
            glVertex3f(i, 5, 0)
        glEnd()

        glBegin(GL_LINES)
        glColor3f(1, 1, 1)
        glVertex3f(–5, 0, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(0, –5, 0)
        glVertex3f(0, 0, 0)

        glColor3f(1, 0, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(5, 0, 0)
        glColor3f(0, 1, 0)
        glVertex3f(0, 0, 0)
        glVertex3f(0, 0, 5)
        glColor3f(0, 0, 1)
        glVertex3f(0, 0, 0)
        glVertex3f(0, 5, 0)
        glEnd()

    def line(p0, p1, color=None):
        c = color or glm.vec3(1, 1, 1)
        glColor3f(c.x, c.y, c.z)
        glVertex3f(p0.x, p0.y, p0.z)
        glVertex3f(p1.x, p1.y, p1.z)

    def grid(segment_count=10, spacing=1, yup=True):
        size = segment_count * spacing
        right = glm.vec3(1, 0, 0)
        forward = glm.vec3(0, 0, 1) if yup else glm.vec3(0, 1, 0)
        x_axis = right * size
        z_axis = forward * size

        data = []
        i = -segment_count

        glBegin(GL_LINES)
        while i <= segment_count:
            p0 = -x_axis + forward * i * spacing
            p1 = x_axis + forward * i * spacing
            line(p0, p1)
            p0 = -z_axis + right * i * spacing
            p1 = z_axis + right * i * spacing
            line(p0, p1)
            i += 1
        glEnd()

    def axis(size=1.0, yup=True):
        right = glm.vec3(1, 0, 0)
        forward = glm.vec3(0, 0, 1) if yup else glm.vec3(0, 1, 0)
        x_axis = right * size
        z_axis = forward * size
        y_axis = glm.cross(forward, right) * size
        glBegin(GL_LINES)
        line(x_axis, glm.vec3(0, 0, 0), glm.vec3(1, 0, 0))
        line(y_axis, glm.vec3(0, 0, 0), glm.vec3(0, 1, 0))
        line(z_axis, glm.vec3(0, 0, 0), glm.vec3(0, 0, 1))
        glEnd()

    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)
            glutMouseWheelFunc(self.controller.glut_mouse_wheel)
            glutKeyboardFunc(self.keyboard_func)
            glutIdleFunc(self.idle_func)

        def keyboard_func(self, *args):
            try:
                key = args[0].decode("utf8")

                if key =="//x1b":
                    glutLeaveMainLoop()

                if key in [‘1’, ‘2’, ‘3’, ‘4’]:
                    if key == ‘1’:
                        self.index_camera ="Skatic"
                    elif key == ‘2’:
                        self.index_camera ="BPL"
                    elif key == ‘3’:
                        self.index_camera ="Rabbid76_v1"
                    elif key == ‘4’:
                        self.index_camera ="Rabbid76_v2"

                    self.camera = self.cameras[self.index_camera]
                    self.controller.camera = self.camera

                if key in [‘o’, ‘p’]:
                    self.camera.eye = glm.vec3(0, 10, 10)
                    self.camera.target = glm.vec3(0, 0, 0)

                    if key == ‘o’:
                        self.yup = True
                        # self.camera.up = glm.vec3(0, 0, 1)
                    elif key == ‘p’:
                        self.yup = False
                        # self.camera.up = glm.vec3(0, 1, 0)

                    self.camera.target = glm.vec3(0, 0, 0)

            except Exception as e:
                import traceback
                traceback.print_exc()

        def startup(self):
            glEnable(GL_DEPTH_TEST)

            aspect = self.width / self.height
            params = {
               "eye": glm.vec3(0, 100, 100),
               "target": glm.vec3(0, 0, 0),
               "up": glm.vec3(0, 1, 0)
            }
            self.cameras = {
               "Skatic": CameraSkatic(**params),
               "BPL": CameraBPL(**params),
               "Rabbid76_v1": CameraRabbid76_v1(**params),
               "Rabbid76_v2": CameraRabbid76_v2(**params)
            }
            self.index_camera ="BPL"
            self.yup = True
            self.camera = self.cameras[self.index_camera]
            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)

            self.camera.load_projection()
            self.camera.load_modelview()

            glLineWidth(5)
            axis(size=70, yup=self.yup)
            glLineWidth(1)
            grid(segment_count=7, spacing=10, yup=self.yup)

            glMatrixMode(GL_PROJECTION)
            glLoadIdentity()
            glOrtho(–1, 1, –1, 1, –1, 1)
            glMatrixMode(GL_MODELVIEW)
            glLoadIdentity()

            info ="/
    "    .join([
               "1: Skatic Camera",
               "2: BPL Camera",
               "3: Rabbid76 Camera (version1)",
               "4: Rabbid76 Camera (version2)",
               "o: RHS Scene Y-UP",
               "p: RHS Scene Z-UP",
            ])
            render_text(–1.0, 1.0 – 0.1, info)
            render_text(–1.0, –1.0,"{} camera is active, scene is {}".format(self.index_camera,"Y-UP" if self.yup else"Z-UP"))

            glutSwapBuffers()

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

    有这么多重新发明轮子的方法不是吗？这是一个简洁的选项(改编自 Opengl Development Cookbook，M.M.Movania，第 2 章中的目标相机概念)：

  • 首先创建新的方向(旋转)矩阵(更新为使用累积的鼠标增量)

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    # global variables somewhere appropriate (or class variables)
    mouseX = 0.0
    mouseY = 0.0
    def rotate_around_target(self, target, delta):
        global mouseX
        global mouseY
        mouseX += delta.x/5.0
        mouseY += delta.y/5.0
        glm::mat4 M = glm::mat4(1)
        M = glm::rotate(M, delta.z, glm::vec3(0, 0, 1))
        M = glm::rotate(M, mouseX , glm::vec3(0, 1, 0))
        M = glm::rotate(M, mouseY, glm::vec3(1, 0, 0))

  • 利用距离得到一个向量，然后通过当前的旋转矩阵平移这个向量

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        self.target = target
        float distance = glm::distance(self.target, self.eye)
        glm::vec3 T = glm::vec3(0, 0, distance)
        T = glm::vec3(M*glm::vec4(T, 0.0f))

  • 通过将平移向量添加到目标位置来获取新的相机眼睛位置

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        self.eye = self.target + T

  • 重新计算正交基(你只需要做 UP 向量)

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        # assuming self.original_up = glm::vec3(0, 1, 0)
        self.up = glm::vec3(M*glm::vec4(self.original_up, 0.0f))
        # or
        self.up = glm::vec3(M*glm::vec4(glm::vec3(0, 1, 0), 0.0f))

    • 5…然后您可以通过使用lookAt函数更新视图矩阵来尝试一下

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        self.view = glm.lookAt( self.eye, self.target, self.up)

    这是迄今为止我发现的这类转换问题/解决方案中最简单的概念。我在 C/C 中对其进行了测试，并为您将其修改为 pyopengl 语法(我真诚地希望如此)。让我们知道(或不)进展如何。

    原创文章，作者：ItWorker，如若转载，请注明出处：https://blog.ytso.com/268004.html

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