如何在3dsMax中实现缩放鼠标？

Question

当你通过移动鼠标滚轮放大/缩小时，我试图模仿3ds max的行为。在3ds max中，此缩放将朝向鼠标位置。到目前为止，我已经想出了这个小小的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()

在此片段中，您可以通过按“1”或“2”键在2种缩放模式之间切换。

当按'1'时，我正在进行标准缩放，到目前为止一直很好。

问题是当按'2'时，在这种情况下我试图将这个thread中的代码改编为python / pyopengl / pygml但是因为我不太清楚这个答案的基础数学我不太清楚如何修复不良行为。

你如何修复发布的代码，以便像3dsmax一样正确地放大/缩小鼠标？

Answer 1

一种可能的解决方案是沿着光线移动摄像机，从摄像机位置到光标（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是“未投影”（unProject）。

计算世界空间中的光标位置（例如在远处平面上）：

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

从眼睛位置到光标的光线由从眼睛位置到世界空间光标位置的归一化矢量给出：

ray_cursor = normalize(pt_world - self.eye)

当您从视口矩形获取窗口高度时，代码中存在一个问题，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

功能zoom_towards_cursor的完整代码清单：

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 

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