从鼠标位置计算和绘制网格表面上的 3D 点
Computing&Plotting 3D Points on Surface of a Mesh from mouse position
我需要在网格表面绘制一组 3D 点（可能是 curve/fonts）以便稍后可以检索它们，因此在纹理上渲染点和附加纹理不起作用。点击鼠标点数drawed/edited。这是用于 CAD 目的，因此精度很重要。
如何从 2D 鼠标位置获取网格局部坐标中的 3D 顶点？
我正在使用 OpenGL 渲染部分，其中透视投影是使用 glm::perspective() 创建的：
FOV = 45.0f
aspect ratio = 16 : 9
zNear = 0.1f
zFar = 100.0f
triangulated mesh
是否可以在对象中进行射线-三角形交点计算space？
相机位置（原点）是否必须是世界Space？
你需要的是（假设旧 api OpenGL 默认符号）：
- 透视投影：
FOVx,FOVy,znear
Model*View 矩阵的逆- 鼠标位置转换为
<-1,+1>范围
- 你的网格组成的三角形列表
你可以这样做：
- 从相机原点投射光线
- 将其转换为网格局部坐标
- 计算最近的ray/triangle交点
是的，您可以在网格局部坐标中计算它，是的，在这种情况下，您需要相同坐标中的 Ray。
这里简单的C++/old api OpenGL/VCL例子：
//---------------------------------------------------------------------------
#include <vcl.h>
#include <math.h>
#include "gl_simple.h"
#include "GLSL_math.h"
#pragma hdrstop
#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
float mx=0.0,my=0.0; // mouse position
//---------------------------------------------------------------------------
// Icosahedron
#define icoX .525731112119133606
#define icoZ .850650808352039932
const GLfloat vdata[12][3] =
{
{-icoX,0.0,icoZ}, {icoX,0.0,icoZ}, {-icoX,0.0,-icoZ}, {icoX,0.0,-icoZ},
{0.0,icoZ,icoX}, {0.0,icoZ,-icoX}, {0.0,-icoZ,icoX}, {0.0,-icoZ,-icoX},
{icoZ,icoX,0.0}, {-icoZ,icoX,0.0}, {icoZ,-icoX,0.0}, {-icoZ,-icoX,0.0},
};
const int tindices=20;
const GLuint tindice[tindices][3] =
{
{0,4,1}, {0,9,4}, {9,5,4}, {4,5,8}, {4,8,1},
{8,10,1}, {8,3,10}, {5,3,8}, {5,2,3}, {2,7,3},
{7,10,3}, {7,6,10}, {7,11,6}, {11,0,6}, {0,1,6},
{6,1,10}, {9,0,11}, {9,11,2}, {9,2,5}, {7,2,11}
};
//---------------------------------------------------------------------------
void icosahedron_draw() // renders mesh using old api
{
int i;
GLfloat nx,ny,nz;
glEnable(GL_CULL_FACE);
glFrontFace(GL_CW);
glBegin(GL_TRIANGLES);
for (i=0;i<tindices;i++)
{
nx =vdata[tindice[i][0]][0];
ny =vdata[tindice[i][0]][1];
nz =vdata[tindice[i][0]][2];
nx+=vdata[tindice[i][1]][0];
ny+=vdata[tindice[i][1]][1];
nz+=vdata[tindice[i][1]][2];
nx+=vdata[tindice[i][2]][0]; nx/=3.0;
ny+=vdata[tindice[i][2]][1]; ny/=3.0;
nz+=vdata[tindice[i][2]][2]; nz/=3.0;
glNormal3f(nx,ny,nz);
glVertex3fv(vdata[tindice[i][0]]);
glVertex3fv(vdata[tindice[i][1]]);
glVertex3fv(vdata[tindice[i][2]]);
}
glEnd();
}
//---------------------------------------------------------------------------
vec3 ray_pick(float mx,float my,mat4 _mv) // return closest intersection using mouse mx,my <-1,+1> position and inverse of ModelView _mv
{
// Perspective settings
const float deg=M_PI/180.0;
const float _zero=1e-6;
float znear=0.1;
float FOVy=45.0*deg;
float FOVx=FOVy*xs/ys; // use aspect ratio if you do not know screen resolution
// Ray endpoints in camera local coordinates
vec3 pos=vec3(mx*tan(0.5*FOVx)*znear,my*tan(0.5*FOVy)*znear,-znear);
vec3 dir=vec3(0.0,0.0,0.0);
// Transform to mesh local coordinates
pos=(_mv*vec4(pos,1.0)).xyz;
dir=(_mv*vec4(dir,1.0)).xyz;
// convert endpoint to direction
dir=normalize(pos-dir);
// needed variables
vec3 pnt=vec3(0.0,0.0,0.0);
vec3 v0,v1,v2,e1,e2,n,p,q,r;
int i,ii=1;
float t=-1.0,tt=-1.0,u,v,det,idet;
// loop through all triangles
for (int i=0;i<tindices;i++)
{
// load v0,v1,v2 with actual triangle
v0.x=vdata[tindice[i][0]][0];
v0.y=vdata[tindice[i][0]][1];
v0.z=vdata[tindice[i][0]][2];
v1.x=vdata[tindice[i][1]][0];
v1.y=vdata[tindice[i][1]][1];
v1.z=vdata[tindice[i][1]][2];
v2.x=vdata[tindice[i][2]][0];
v2.y=vdata[tindice[i][2]][1];
v2.z=vdata[tindice[i][2]][2];
//compute ray(pos,dir) triangle(v0,v1,v2) intersection
e1=v1-v0;
e2=v2-v0;
// Calculate planes normal vector
p=cross(dir,e2);
det=dot(e1,p);
// Ray is parallel to plane
if (abs(det)<1e-8) continue;
idet=1.0/det;
r=pos-v0;
u=dot(r,p)*idet;
if ((u<0.0)||(u>1.0)) continue;
q=cross(r,e1);
v=dot(dir,q)*idet;
if ((v<0.0)||(u+v>1.0)) continue;
t=dot(e2,q)*idet;
// remember closest intersection to camera
if ((t>_zero)&&((t<=tt)||(ii!=0)))
{
ii=0; tt=t;
// barycentric interpolate position
t=1.0-u-v;
pnt=(v0*t)+(v1*u)+(v2*v);
}
}
return pnt; // if (ii==1) no intersection found
}
//---------------------------------------------------------------------------
void gl_draw()
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glDisable(GL_TEXTURE_2D);
glEnable(GL_DEPTH_TEST);
glEnable(GL_LIGHT0);
glEnable(GL_CULL_FACE);
// glDisable(GL_CULL_FACE);
glFrontFace(GL_CCW);
glEnable(GL_COLOR_MATERIAL);
/*
glPolygonMode(GL_FRONT,GL_FILL);
glPolygonMode(GL_BACK,GL_LINE);
glDisable(GL_CULL_FACE);
*/
// set projection
glMatrixMode(GL_PROJECTION); // operacie s projekcnou maticou
glLoadIdentity(); // jednotkova matica projekcie
gluPerspective(45,float(xs)/float(ys),0.1,100.0); // matica=perspektiva,120 stupnov premieta z viewsize do 0.1
// set view
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.2,0.0,-5.0);
static float ang=0.0;
glRotatef(ang,0.2,0.7,0.2); ang+=5.0; if (ang>=360.0) ang-=360.0;
// obtain actual modelview matrix (mv) and its inverse (_mv)
mat4 mv,_mv;
float m[16];
glGetFloatv(GL_MODELVIEW_MATRIX,m);
mv.set(m);
_mv=inverse(mv);
// render mesh
glColor3f(0.5,0.5,0.5);
glEnable(GL_LIGHTING);
icosahedron_draw();
glDisable(GL_LIGHTING);
// get point mouse points to
vec3 p=ray_pick(mx,my,_mv);
// render it for visual check
float r=0.1;
glColor3f(1.0,1.0,0.0);
glBegin(GL_LINES);
glVertex3f(p.x-r,p.y,p.z); glVertex3f(p.x+r,p.y,p.z);
glVertex3f(p.x,p.y-r,p.z); glVertex3f(p.x,p.y+r,p.z);
glVertex3f(p.x,p.y,p.z-r); glVertex3f(p.x,p.y,p.z+r);
glEnd();
// glFlush();
glFinish();
SwapBuffers(hdc);
}
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner):TForm(Owner)
{
// Init of program
gl_init(Handle); // init OpenGL
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormDestroy(TObject *Sender)
{
// Exit of program
gl_exit();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormPaint(TObject *Sender)
{
// repaint
gl_draw();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormResize(TObject *Sender)
{
// resize
gl_resize(ClientWidth,ClientHeight);
}
//---------------------------------------------------------------------------
void __fastcall TForm1::tim_redrawTimer(TObject *Sender)
{
gl_draw();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormMouseMove(TObject *Sender, TShiftState Shift, int X, int Y)
{
// just event to obtain actual mouse position
// and convert it from screen coordinates <0,xs),<0,ys) to <-1,+1> range
mx=X; mx=(2.0*mx/float(xs-1))-1.0;
my=Y; my=1.0-(2.0*my/float(ys-1)); // y is mirrored in OpenGL
}
//---------------------------------------------------------------------------
唯一重要的是函数 ray_pick，它 returns 您的 3D 点基于鼠标 2D 位置和 ModelView 矩阵的实际逆...
此处预览：
我在找到的 3D 位置渲染黄色十字，因为你可以看到它与表面直接接触（因为它的一半线在表面以下）。
除了常用的东西之外，我还使用了我的库： for the OpenGL context creation and GLSL_math.h 而不是 GLM 用于矢量和矩阵数学。但是无论如何都可以创建 GL 上下文，你也可以使用你拥有的数学知识（我认为甚至语法与 GLM 相同，因为他们也试图模仿 GLSL...）
看起来像方面 1:1 这完美地工作，并且在矩形方面它离屏幕中心越远它稍微不精确（很可能是因为我使用了原始 gluPerspective 有一些不精确的术语在其中，或者我在创建光线时错过了一些修正，但我对此表示怀疑）
如果你不需要高精度（不是你的情况，因为 CAD/CAM 需要尽可能高的精度）你可以摆脱光线网格交叉并直接在鼠标位置选择深度缓冲区和从中计算结果点（不需要网格）。
有关更多信息，请参阅相关 QA：
我需要在网格表面绘制一组 3D 点（可能是 curve/fonts）以便稍后可以检索它们，因此在纹理上渲染点和附加纹理不起作用。点击鼠标点数drawed/edited。这是用于 CAD 目的，因此精度很重要。
如何从 2D 鼠标位置获取网格局部坐标中的 3D 顶点？
我正在使用 OpenGL 渲染部分，其中透视投影是使用
glm::perspective()创建的：FOV = 45.0f aspect ratio = 16 : 9 zNear = 0.1f zFar = 100.0f triangulated mesh是否可以在对象中进行射线-三角形交点计算space？
相机位置（原点）是否必须是世界Space？
你需要的是（假设旧 api OpenGL 默认符号）：
- 透视投影：
FOVx,FOVy,znear Model*View矩阵的逆- 鼠标位置转换为
<-1,+1>范围 - 你的网格组成的三角形列表
你可以这样做：
- 从相机原点投射光线
- 将其转换为网格局部坐标
- 计算最近的ray/triangle交点
是的，您可以在网格局部坐标中计算它，是的，在这种情况下，您需要相同坐标中的 Ray。
这里简单的C++/old api OpenGL/VCL例子：
//---------------------------------------------------------------------------
#include <vcl.h>
#include <math.h>
#include "gl_simple.h"
#include "GLSL_math.h"
#pragma hdrstop
#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
float mx=0.0,my=0.0; // mouse position
//---------------------------------------------------------------------------
// Icosahedron
#define icoX .525731112119133606
#define icoZ .850650808352039932
const GLfloat vdata[12][3] =
{
{-icoX,0.0,icoZ}, {icoX,0.0,icoZ}, {-icoX,0.0,-icoZ}, {icoX,0.0,-icoZ},
{0.0,icoZ,icoX}, {0.0,icoZ,-icoX}, {0.0,-icoZ,icoX}, {0.0,-icoZ,-icoX},
{icoZ,icoX,0.0}, {-icoZ,icoX,0.0}, {icoZ,-icoX,0.0}, {-icoZ,-icoX,0.0},
};
const int tindices=20;
const GLuint tindice[tindices][3] =
{
{0,4,1}, {0,9,4}, {9,5,4}, {4,5,8}, {4,8,1},
{8,10,1}, {8,3,10}, {5,3,8}, {5,2,3}, {2,7,3},
{7,10,3}, {7,6,10}, {7,11,6}, {11,0,6}, {0,1,6},
{6,1,10}, {9,0,11}, {9,11,2}, {9,2,5}, {7,2,11}
};
//---------------------------------------------------------------------------
void icosahedron_draw() // renders mesh using old api
{
int i;
GLfloat nx,ny,nz;
glEnable(GL_CULL_FACE);
glFrontFace(GL_CW);
glBegin(GL_TRIANGLES);
for (i=0;i<tindices;i++)
{
nx =vdata[tindice[i][0]][0];
ny =vdata[tindice[i][0]][1];
nz =vdata[tindice[i][0]][2];
nx+=vdata[tindice[i][1]][0];
ny+=vdata[tindice[i][1]][1];
nz+=vdata[tindice[i][1]][2];
nx+=vdata[tindice[i][2]][0]; nx/=3.0;
ny+=vdata[tindice[i][2]][1]; ny/=3.0;
nz+=vdata[tindice[i][2]][2]; nz/=3.0;
glNormal3f(nx,ny,nz);
glVertex3fv(vdata[tindice[i][0]]);
glVertex3fv(vdata[tindice[i][1]]);
glVertex3fv(vdata[tindice[i][2]]);
}
glEnd();
}
//---------------------------------------------------------------------------
vec3 ray_pick(float mx,float my,mat4 _mv) // return closest intersection using mouse mx,my <-1,+1> position and inverse of ModelView _mv
{
// Perspective settings
const float deg=M_PI/180.0;
const float _zero=1e-6;
float znear=0.1;
float FOVy=45.0*deg;
float FOVx=FOVy*xs/ys; // use aspect ratio if you do not know screen resolution
// Ray endpoints in camera local coordinates
vec3 pos=vec3(mx*tan(0.5*FOVx)*znear,my*tan(0.5*FOVy)*znear,-znear);
vec3 dir=vec3(0.0,0.0,0.0);
// Transform to mesh local coordinates
pos=(_mv*vec4(pos,1.0)).xyz;
dir=(_mv*vec4(dir,1.0)).xyz;
// convert endpoint to direction
dir=normalize(pos-dir);
// needed variables
vec3 pnt=vec3(0.0,0.0,0.0);
vec3 v0,v1,v2,e1,e2,n,p,q,r;
int i,ii=1;
float t=-1.0,tt=-1.0,u,v,det,idet;
// loop through all triangles
for (int i=0;i<tindices;i++)
{
// load v0,v1,v2 with actual triangle
v0.x=vdata[tindice[i][0]][0];
v0.y=vdata[tindice[i][0]][1];
v0.z=vdata[tindice[i][0]][2];
v1.x=vdata[tindice[i][1]][0];
v1.y=vdata[tindice[i][1]][1];
v1.z=vdata[tindice[i][1]][2];
v2.x=vdata[tindice[i][2]][0];
v2.y=vdata[tindice[i][2]][1];
v2.z=vdata[tindice[i][2]][2];
//compute ray(pos,dir) triangle(v0,v1,v2) intersection
e1=v1-v0;
e2=v2-v0;
// Calculate planes normal vector
p=cross(dir,e2);
det=dot(e1,p);
// Ray is parallel to plane
if (abs(det)<1e-8) continue;
idet=1.0/det;
r=pos-v0;
u=dot(r,p)*idet;
if ((u<0.0)||(u>1.0)) continue;
q=cross(r,e1);
v=dot(dir,q)*idet;
if ((v<0.0)||(u+v>1.0)) continue;
t=dot(e2,q)*idet;
// remember closest intersection to camera
if ((t>_zero)&&((t<=tt)||(ii!=0)))
{
ii=0; tt=t;
// barycentric interpolate position
t=1.0-u-v;
pnt=(v0*t)+(v1*u)+(v2*v);
}
}
return pnt; // if (ii==1) no intersection found
}
//---------------------------------------------------------------------------
void gl_draw()
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glDisable(GL_TEXTURE_2D);
glEnable(GL_DEPTH_TEST);
glEnable(GL_LIGHT0);
glEnable(GL_CULL_FACE);
// glDisable(GL_CULL_FACE);
glFrontFace(GL_CCW);
glEnable(GL_COLOR_MATERIAL);
/*
glPolygonMode(GL_FRONT,GL_FILL);
glPolygonMode(GL_BACK,GL_LINE);
glDisable(GL_CULL_FACE);
*/
// set projection
glMatrixMode(GL_PROJECTION); // operacie s projekcnou maticou
glLoadIdentity(); // jednotkova matica projekcie
gluPerspective(45,float(xs)/float(ys),0.1,100.0); // matica=perspektiva,120 stupnov premieta z viewsize do 0.1
// set view
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.2,0.0,-5.0);
static float ang=0.0;
glRotatef(ang,0.2,0.7,0.2); ang+=5.0; if (ang>=360.0) ang-=360.0;
// obtain actual modelview matrix (mv) and its inverse (_mv)
mat4 mv,_mv;
float m[16];
glGetFloatv(GL_MODELVIEW_MATRIX,m);
mv.set(m);
_mv=inverse(mv);
// render mesh
glColor3f(0.5,0.5,0.5);
glEnable(GL_LIGHTING);
icosahedron_draw();
glDisable(GL_LIGHTING);
// get point mouse points to
vec3 p=ray_pick(mx,my,_mv);
// render it for visual check
float r=0.1;
glColor3f(1.0,1.0,0.0);
glBegin(GL_LINES);
glVertex3f(p.x-r,p.y,p.z); glVertex3f(p.x+r,p.y,p.z);
glVertex3f(p.x,p.y-r,p.z); glVertex3f(p.x,p.y+r,p.z);
glVertex3f(p.x,p.y,p.z-r); glVertex3f(p.x,p.y,p.z+r);
glEnd();
// glFlush();
glFinish();
SwapBuffers(hdc);
}
//---------------------------------------------------------------------------
__fastcall TForm1::TForm1(TComponent* Owner):TForm(Owner)
{
// Init of program
gl_init(Handle); // init OpenGL
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormDestroy(TObject *Sender)
{
// Exit of program
gl_exit();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormPaint(TObject *Sender)
{
// repaint
gl_draw();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormResize(TObject *Sender)
{
// resize
gl_resize(ClientWidth,ClientHeight);
}
//---------------------------------------------------------------------------
void __fastcall TForm1::tim_redrawTimer(TObject *Sender)
{
gl_draw();
}
//---------------------------------------------------------------------------
void __fastcall TForm1::FormMouseMove(TObject *Sender, TShiftState Shift, int X, int Y)
{
// just event to obtain actual mouse position
// and convert it from screen coordinates <0,xs),<0,ys) to <-1,+1> range
mx=X; mx=(2.0*mx/float(xs-1))-1.0;
my=Y; my=1.0-(2.0*my/float(ys-1)); // y is mirrored in OpenGL
}
//---------------------------------------------------------------------------
唯一重要的是函数 ray_pick，它 returns 您的 3D 点基于鼠标 2D 位置和 ModelView 矩阵的实际逆...
此处预览：
我在找到的 3D 位置渲染黄色十字，因为你可以看到它与表面直接接触（因为它的一半线在表面以下）。
除了常用的东西之外，我还使用了我的库：
看起来像方面 1:1 这完美地工作，并且在矩形方面它离屏幕中心越远它稍微不精确（很可能是因为我使用了原始 gluPerspective 有一些不精确的术语在其中，或者我在创建光线时错过了一些修正，但我对此表示怀疑）
如果你不需要高精度（不是你的情况，因为 CAD/CAM 需要尽可能高的精度）你可以摆脱光线网格交叉并直接在鼠标位置选择深度缓冲区和从中计算结果点（不需要网格）。
有关更多信息，请参阅相关 QA：