python - 如何像在 3dsMax 中一样实现对鼠标的缩放？

Question

当您通过移动鼠标滚轮放大/缩小时，我试图模仿 3dsmax 的行为。在 3ds max 中，此缩放将朝向鼠标位置。到目前为止，我想出了这个小 mcve:

import math
from ctypes import c_void_p

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


class Camera():

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

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

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

    def zoom_towards_cursor(self, *args):
        x = args[2]
        y = args[3]
        v = glGetIntegerv(GL_VIEWPORT)
        viewport = vec4(float(v[0]), float(v[1]), float(v[2]), float(v[3]))
        height = viewport.z

        p0 = vec3(x, height - y, 0.0)
        p1 = vec3(x, height - y, 1.0)
        v1 = unProject(p0, self.view, self.projection, viewport)
        v2 = unProject(p1, self.view, self.projection, viewport)

        world_from = vec3(
            (-v1.z * (v2.x - v1.x)) / (v2.z - v1.z) + v1.x,
            (-v1.z * (v2.y - v1.y)) / (v2.z - v1.z) + v1.y,
            0.0
        )

        self.eye.z = self.eye.z * (1.0 + 0.1 * args[1])

        view = lookAt(self.eye, self.target, self.up)
        v1 = unProject(p0, view, self.projection, viewport)
        v2 = unProject(p1, view, self.projection, viewport)

        world_to = vec3(
            (v1.z * (v2.x - v1.x)) / (v2.z - v1.z) + v1.x,
            (-v1.z * (v2.y - v1.y)) / (v2.z - v1.z) + v1.y,
            0.0
        )

        offset = world_to - world_from
        print(self.eye.z, world_from, world_to, offset)

        self.eye += offset
        self.target += offset


class GlutController():

    def __init__(self, camera):
        self.camera = camera
        self.zoom = self.camera.zoom

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


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)
        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']:
                self.controller.zoom = self.camera.zoom
                print("Using normal zoom")
            elif key in ['2']:
                self.controller.zoom = self.camera.zoom_towards_cursor
                print("Using zoom towards mouse")

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

    def startup(self):
        glEnable(GL_DEPTH_TEST)

        aspect = self.width / self.height
        params = {
            "eye": vec3(10, 10, 10),
            "target": vec3(0, 0, 0),
            "up": vec3(0, 1, 0)
        }
        self.cameras = [
            Camera(**params)
        ]
        self.camera = self.cameras[0]
        self.model = 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(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, 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()

        glutSwapBuffers()


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

在此代码段中，您可以通过按“1”键或“2”键在 2 种缩放模式之间切换。

当按下“1”时，我正在执行标准缩放，到目前为止一切顺利。

问题出在按“2”时，在这种情况下，我尝试改编此 thread 中的代码到 python/pyopengl/pygml，但因为我不太了解该答案的基本数学原理，所以我不太清楚如何解决不良行为。

您将如何修复发布的代码，使其像 3dsmax 一样正确地放大/缩小鼠标？

Answer 1

一个可能的解决方案是沿着一条射线移动相机，从相机位置通过光标(鼠标)位置并平行移动目标位置。

self.eye    = self.eye    + ray_cursor * delta
self.target = self.target + ray_cursor * delta

为此，光标的窗口位置必须“未投影”(unProject)。

计算光标在世界空间中的位置(例如在远平面上):

pt_wnd   = vec3(x, height - y, 1.0)
pt_world = unProject(pt_wnd, self.view, self.projection, viewport)

从眼睛位置通过光标的光线由从眼睛位置到世界空间光标位置的归一化向量给出:

ray_cursor = normalize(pt_world - self.eye)

当您从视口(viewport)矩形获取窗口高度时，您的代码中存在问题，因为高度是 .w 组件而不是 .z 组件:

v = glGetIntegerv(GL_VIEWPORT)
viewport = vec4(float(v[0]), float(v[1]), float(v[2]), float(v[3]))
width  = viewport.z
height = viewport.w

zoom_towards_cursor 函数的完整代码 list :

def zoom_towards_cursor(self, *args):
    x = args[2]
    y = args[3]
    v = glGetIntegerv(GL_VIEWPORT)
    viewport = vec4(float(v[0]), float(v[1]), float(v[2]), float(v[3]))
    width  = viewport.z
    height = viewport.w

    pt_wnd     = vec3(x, height - y, 1.0)
    pt_world   = unProject(pt_wnd, self.view, self.projection, viewport)
    ray_cursor = normalize(pt_world - self.eye)

    delta = -args[1]
    self.eye    = self.eye    + ray_cursor * delta
    self.target = self.target + ray_cursor * delta 

另见 Python OpenGL 4.6, GLM navigation

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