正确处理相机旋转的方法
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)
)
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。
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 mathfrom 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
回答：
我建议围绕视图空间中的轴进行旋转
您必须知道视图矩阵（V）。由于视图矩阵被编码在self.eye，self.target并且self.up，它必须由计算lookAt：
V = glm.lookAt(self.eye, self.target, self.up)计算pivot视图空间，旋转角度和旋转轴。在这种情况下，轴是向右旋转的方向，其中y轴必须翻转：
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并计算围绕枢轴的比率矩阵RP。最后V通过旋转矩阵变换视图矩阵（）。结果是新的视图矩阵NV：
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
解码self.eye，self.target然后self.up从新的视图矩阵中进行解码NV：
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])
该方法的完整编码 rotate_around_target_view：
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])
最终，它可以绕世界原点和眼睛位置甚至任何其他点旋转。
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，因此不必将轴转换为视图空间，并且将旋转应用于视图矩阵（NV = V *
RP）之前：
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)
当然，两种解决方案都可以结合使用。通过垂直（上下）拖动，视图可以在其水平轴上旋转。通过水平拖动（左右），模型（世界）可以绕其（上）轴旋转：
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))
考虑到问题的原始代码，为了实现最小程度的侵入性方法，我将提出以下建议：
操作之后，视图的目标应该是
target函数的输入参数rotate_around_target。鼠标水平移动应使视图围绕世界的向上矢量旋转
垂直鼠标移动应使视图围绕当前水平轴倾斜
我想出了以下方法：
计算当前视线（
los），向上矢量（up）和水平轴（right）通过将向上矢量投影到由原始向上矢量和当前视线给定的平面上，将向上矢量垂直放置。这是通过Gram–Schmidt正交化得到的。
绕当前水平轴倾斜。这意味着
los并up绕right轴旋转。围绕上向量旋转。
los并right旋转up。计算设置向上并计算眼睛和目标位置，其中目标由输入参数target设置：
def rotate_around_target(self, target, delta):
# get directionslos = 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
以上是 正确处理相机旋转的方法 的全部内容， 来源链接： utcz.com/qa/418118.html
