如何在OpenGL中绘制视锥
Krythic
我使用C＃和OpenTK创建了一个视锥类，它运行良好。但是，我希望能够绘制平截头体的边界以用于调试。我不知道如何从Matrix数据中获取顶点数据以进行绘制。我只是想知道是否有人知道怎么做。
这是我的视锥课程：
using System;
using GrimoireGDK.GameDevelopmentKit.Math.Geometry;
using OpenTK;
namespace GrimoireGameClient.Client.Window.Bindings {
public class Frustum {
private float[] _clipMatrix = new float[ 16 ];
private float[ , ] _frustum = new float[ 6 , 4 ];
public const int A = 0;
public const int B = 1;
public const int C = 2;
public const int D = 3;
public enum ClippingPlane : int {
Right = 0 ,
Left = 1 ,
Bottom = 2 ,
Top = 3 ,
Back = 4 ,
Front = 5
}
private void NormalizePlane( float[ , ] frustum , int side ) {
float magnitude = ( float )Math.Sqrt( ( frustum[ side , 0 ] * frustum[ side , 0 ] ) + ( frustum[ side , 1 ] * frustum[ side , 1 ] )
+ ( frustum[ side , 2 ] * frustum[ side , 2 ] ) );
frustum[ side , 0 ] /= magnitude;
frustum[ side , 1 ] /= magnitude;
frustum[ side , 2 ] /= magnitude;
frustum[ side , 3 ] /= magnitude;
}
public bool PointVsFrustum( float x , float y , float z ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( this._frustum[ i , 0 ] * x + this._frustum[ i , 1 ] * y + this._frustum[ i , 2 ] * z + this._frustum[ i , 3 ] <= 0.0f ) {
return false;
}
}
return true;
}
public bool PointVsFrustum( Vector3 location ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( this._frustum[ i , 0 ] * location.X + this._frustum[ i , 1 ] * location.Y + this._frustum[ i , 2 ] * location.Z + this._frustum[ i , 3 ] <= 0.0f ) {
return false;
}
}
return true;
}
public bool SphereVsFrustum( float x , float y , float z , float radius ) {
float d = 0;
for( int p = 0 ; p < 6 ; p++ ) {
d = _frustum[ p , 0 ] * x + _frustum[ p , 1 ] * y + _frustum[ p , 2 ] * z + _frustum[ p , 3 ];
if( d <= -radius ) {
return false;
}
}
return true;
}
public bool SphereVsFrustum( Vector3 location , float radius ) {
float d = 0;
for( int p = 0 ; p < 6 ; p++ ) {
d = _frustum[ p , 0 ] * location.X + _frustum[ p , 1 ] * location.Y + _frustum[ p , 2 ] * location.Z + _frustum[ p , 3 ];
if( d <= -radius ) {
return false;
}
}
return true;
}
public bool VolumeVsFrustum( float x , float y , float z , float width , float height , float length ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( _frustum[ i , A ] * ( x - width ) + _frustum[ i , B ] * ( y - height ) + _frustum[ i , C ] * ( z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + width ) + _frustum[ i , B ] * ( y - height ) + _frustum[ i , C ] * ( z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - width ) + _frustum[ i , B ] * ( y + height ) + _frustum[ i , C ] * ( z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + width ) + _frustum[ i , B ] * ( y + height ) + _frustum[ i , C ] * ( z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - width ) + _frustum[ i , B ] * ( y - height ) + _frustum[ i , C ] * ( z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + width ) + _frustum[ i , B ] * ( y - height ) + _frustum[ i , C ] * ( z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - width ) + _frustum[ i , B ] * ( y + height ) + _frustum[ i , C ] * ( z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + width ) + _frustum[ i , B ] * ( y + height ) + _frustum[ i , C ] * ( z + length ) + _frustum[ i , D ] > 0 )
continue;
return false;
}
return true;
}
public bool VolumeVsFrustum( Vector3 location, float width , float height , float length ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( _frustum[ i , A ] * ( location.X - width ) + _frustum[ i , B ] * ( location.Y - height ) + _frustum[ i , C ] * ( location.Z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + width ) + _frustum[ i , B ] * ( location.Y - height ) + _frustum[ i , C ] * ( location.Z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - width ) + _frustum[ i , B ] * ( location.Y + height ) + _frustum[ i , C ] * ( location.Z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + width ) + _frustum[ i , B ] * ( location.Y + height ) + _frustum[ i , C ] * ( location.Z - length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - width ) + _frustum[ i , B ] * ( location.Y - height ) + _frustum[ i , C ] * ( location.Z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + width ) + _frustum[ i , B ] * ( location.Y - height ) + _frustum[ i , C ] * ( location.Z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - width ) + _frustum[ i , B ] * ( location.Y + height ) + _frustum[ i , C ] * ( location.Z + length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + width ) + _frustum[ i , B ] * ( location.Y + height ) + _frustum[ i , C ] * ( location.Z + length ) + _frustum[ i , D ] > 0 )
continue;
return false;
}
return true;
}
public bool VolumeVsFrustum( Vector3 location , BoundingVolume volume ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( _frustum[ i , A ] * ( location.X - volume.Width ) + _frustum[ i , B ] * ( location.Y - volume.Height ) + _frustum[ i , C ] * ( location.Z - volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + volume.Width ) + _frustum[ i , B ] * ( location.Y - volume.Height ) + _frustum[ i , C ] * ( location.Z - volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - volume.Width ) + _frustum[ i , B ] * ( location.Y + volume.Height ) + _frustum[ i , C ] * ( location.Z - volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + volume.Width ) + _frustum[ i , B ] * ( location.Y + volume.Height ) + _frustum[ i , C ] * ( location.Z - volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - volume.Width ) + _frustum[ i , B ] * ( location.Y - volume.Height ) + _frustum[ i , C ] * ( location.Z + volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + volume.Width ) + _frustum[ i , B ] * ( location.Y - volume.Height ) + _frustum[ i , C ] * ( location.Z + volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X - volume.Width ) + _frustum[ i , B ] * ( location.Y + volume.Height ) + _frustum[ i , C ] * ( location.Z + volume.Length ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( location.X + volume.Width ) + _frustum[ i , B ] * ( location.Y + volume.Height ) + _frustum[ i , C ] * ( location.Z + volume.Length ) + _frustum[ i , D ] > 0 )
continue;
return false;
}
return true;
}
public bool CubeVsFrustum( float x , float y , float z , float size ) {
for( int i = 0 ; i < 6 ; i++ ) {
if( _frustum[ i , A ] * ( x - size ) + _frustum[ i , B ] * ( y - size ) + _frustum[ i , C ] * ( z - size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + size ) + _frustum[ i , B ] * ( y - size ) + _frustum[ i , C ] * ( z - size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - size ) + _frustum[ i , B ] * ( y + size ) + _frustum[ i , C ] * ( z - size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + size ) + _frustum[ i , B ] * ( y + size ) + _frustum[ i , C ] * ( z - size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - size ) + _frustum[ i , B ] * ( y - size ) + _frustum[ i , C ] * ( z + size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + size ) + _frustum[ i , B ] * ( y - size ) + _frustum[ i , C ] * ( z + size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x - size ) + _frustum[ i , B ] * ( y + size ) + _frustum[ i , C ] * ( z + size ) + _frustum[ i , D ] > 0 )
continue;
if( _frustum[ i , A ] * ( x + size ) + _frustum[ i , B ] * ( y + size ) + _frustum[ i , C ] * ( z + size ) + _frustum[ i , D ] > 0 )
continue;
return false;
}
return true;
}
public void CalculateFrustum( Matrix4 projectionMatrix , Matrix4 modelViewMatrix ) {
_clipMatrix[ 0 ] = ( modelViewMatrix.M11 * projectionMatrix.M11 ) + ( modelViewMatrix.M12 * projectionMatrix.M21 ) + ( modelViewMatrix.M13 * projectionMatrix.M31 ) + ( modelViewMatrix.M14 * projectionMatrix.M41 );
_clipMatrix[ 1 ] = ( modelViewMatrix.M11 * projectionMatrix.M12 ) + ( modelViewMatrix.M12 * projectionMatrix.M22 ) + ( modelViewMatrix.M13 * projectionMatrix.M32 ) + ( modelViewMatrix.M14 * projectionMatrix.M42 );
_clipMatrix[ 2 ] = ( modelViewMatrix.M11 * projectionMatrix.M13 ) + ( modelViewMatrix.M12 * projectionMatrix.M23 ) + ( modelViewMatrix.M13 * projectionMatrix.M33 ) + ( modelViewMatrix.M14 * projectionMatrix.M43 );
_clipMatrix[ 3 ] = ( modelViewMatrix.M11 * projectionMatrix.M14 ) + ( modelViewMatrix.M12 * projectionMatrix.M24 ) + ( modelViewMatrix.M13 * projectionMatrix.M34 ) + ( modelViewMatrix.M14 * projectionMatrix.M44 );
_clipMatrix[ 4 ] = ( modelViewMatrix.M21 * projectionMatrix.M11 ) + ( modelViewMatrix.M22 * projectionMatrix.M21 ) + ( modelViewMatrix.M23 * projectionMatrix.M31 ) + ( modelViewMatrix.M24 * projectionMatrix.M41 );
_clipMatrix[ 5 ] = ( modelViewMatrix.M21 * projectionMatrix.M12 ) + ( modelViewMatrix.M22 * projectionMatrix.M22 ) + ( modelViewMatrix.M23 * projectionMatrix.M32 ) + ( modelViewMatrix.M24 * projectionMatrix.M42 );
_clipMatrix[ 6 ] = ( modelViewMatrix.M21 * projectionMatrix.M13 ) + ( modelViewMatrix.M22 * projectionMatrix.M23 ) + ( modelViewMatrix.M23 * projectionMatrix.M33 ) + ( modelViewMatrix.M24 * projectionMatrix.M43 );
_clipMatrix[ 7 ] = ( modelViewMatrix.M21 * projectionMatrix.M14 ) + ( modelViewMatrix.M22 * projectionMatrix.M24 ) + ( modelViewMatrix.M23 * projectionMatrix.M34 ) + ( modelViewMatrix.M24 * projectionMatrix.M44 );
_clipMatrix[ 8 ] = ( modelViewMatrix.M31 * projectionMatrix.M11 ) + ( modelViewMatrix.M32 * projectionMatrix.M21 ) + ( modelViewMatrix.M33 * projectionMatrix.M31 ) + ( modelViewMatrix.M34 * projectionMatrix.M41 );
_clipMatrix[ 9 ] = ( modelViewMatrix.M31 * projectionMatrix.M12 ) + ( modelViewMatrix.M32 * projectionMatrix.M22 ) + ( modelViewMatrix.M33 * projectionMatrix.M32 ) + ( modelViewMatrix.M34 * projectionMatrix.M42 );
_clipMatrix[ 10 ] = ( modelViewMatrix.M31 * projectionMatrix.M13 ) + ( modelViewMatrix.M32 * projectionMatrix.M23 ) + ( modelViewMatrix.M33 * projectionMatrix.M33 ) + ( modelViewMatrix.M34 * projectionMatrix.M43 );
_clipMatrix[ 11 ] = ( modelViewMatrix.M31 * projectionMatrix.M14 ) + ( modelViewMatrix.M32 * projectionMatrix.M24 ) + ( modelViewMatrix.M33 * projectionMatrix.M34 ) + ( modelViewMatrix.M34 * projectionMatrix.M44 );
_clipMatrix[ 12 ] = ( modelViewMatrix.M41 * projectionMatrix.M11 ) + ( modelViewMatrix.M42 * projectionMatrix.M21 ) + ( modelViewMatrix.M43 * projectionMatrix.M31 ) + ( modelViewMatrix.M44 * projectionMatrix.M41 );
_clipMatrix[ 13 ] = ( modelViewMatrix.M41 * projectionMatrix.M12 ) + ( modelViewMatrix.M42 * projectionMatrix.M22 ) + ( modelViewMatrix.M43 * projectionMatrix.M32 ) + ( modelViewMatrix.M44 * projectionMatrix.M42 );
_clipMatrix[ 14 ] = ( modelViewMatrix.M41 * projectionMatrix.M13 ) + ( modelViewMatrix.M42 * projectionMatrix.M23 ) + ( modelViewMatrix.M43 * projectionMatrix.M33 ) + ( modelViewMatrix.M44 * projectionMatrix.M43 );
_clipMatrix[ 15 ] = ( modelViewMatrix.M41 * projectionMatrix.M14 ) + ( modelViewMatrix.M42 * projectionMatrix.M24 ) + ( modelViewMatrix.M43 * projectionMatrix.M34 ) + ( modelViewMatrix.M44 * projectionMatrix.M44 );
_frustum[ ( int )ClippingPlane.Right , 0 ] = _clipMatrix[ 3 ] - _clipMatrix[ 0 ];
_frustum[ ( int )ClippingPlane.Right , 1 ] = _clipMatrix[ 7 ] - _clipMatrix[ 4 ];
_frustum[ ( int )ClippingPlane.Right , 2 ] = _clipMatrix[ 11 ] - _clipMatrix[ 8 ];
_frustum[ ( int )ClippingPlane.Right , 3 ] = _clipMatrix[ 15 ] - _clipMatrix[ 12 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Right );
_frustum[ ( int )ClippingPlane.Left , 0 ] = _clipMatrix[ 3 ] + _clipMatrix[ 0 ];
_frustum[ ( int )ClippingPlane.Left , 1 ] = _clipMatrix[ 7 ] + _clipMatrix[ 4 ];
_frustum[ ( int )ClippingPlane.Left , 2 ] = _clipMatrix[ 11 ] + _clipMatrix[ 8 ];
_frustum[ ( int )ClippingPlane.Left , 3 ] = _clipMatrix[ 15 ] + _clipMatrix[ 12 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Left );
_frustum[ ( int )ClippingPlane.Bottom , 0 ] = _clipMatrix[ 3 ] + _clipMatrix[ 1 ];
_frustum[ ( int )ClippingPlane.Bottom , 1 ] = _clipMatrix[ 7 ] + _clipMatrix[ 5 ];
_frustum[ ( int )ClippingPlane.Bottom , 2 ] = _clipMatrix[ 11 ] + _clipMatrix[ 9 ];
_frustum[ ( int )ClippingPlane.Bottom , 3 ] = _clipMatrix[ 15 ] + _clipMatrix[ 13 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Bottom );
_frustum[ ( int )ClippingPlane.Top , 0 ] = _clipMatrix[ 3 ] - _clipMatrix[ 1 ];
_frustum[ ( int )ClippingPlane.Top , 1 ] = _clipMatrix[ 7 ] - _clipMatrix[ 5 ];
_frustum[ ( int )ClippingPlane.Top , 2 ] = _clipMatrix[ 11 ] - _clipMatrix[ 9 ];
_frustum[ ( int )ClippingPlane.Top , 3 ] = _clipMatrix[ 15 ] - _clipMatrix[ 13 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Top );
_frustum[ ( int )ClippingPlane.Back , 0 ] = _clipMatrix[ 3 ] - _clipMatrix[ 2 ];
_frustum[ ( int )ClippingPlane.Back , 1 ] = _clipMatrix[ 7 ] - _clipMatrix[ 6 ];
_frustum[ ( int )ClippingPlane.Back , 2 ] = _clipMatrix[ 11 ] - _clipMatrix[ 10 ];
_frustum[ ( int )ClippingPlane.Back , 3 ] = _clipMatrix[ 15 ] - _clipMatrix[ 14 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Back );
_frustum[ ( int )ClippingPlane.Front , 0 ] = _clipMatrix[ 3 ] + _clipMatrix[ 2 ];
_frustum[ ( int )ClippingPlane.Front , 1 ] = _clipMatrix[ 7 ] + _clipMatrix[ 6 ];
_frustum[ ( int )ClippingPlane.Front , 2 ] = _clipMatrix[ 11 ] + _clipMatrix[ 10 ];
_frustum[ ( int )ClippingPlane.Front , 3 ] = _clipMatrix[ 15 ] + _clipMatrix[ 14 ];
NormalizePlane( _frustum , ( int )ClippingPlane.Front );
}
/// <summary>
/// Draw the frustum for debugging purposes.
/// </summary>
public void Draw() {
// Implement drawing code here.
}
}
}
有人知道如何绘制平截头体吗？而且我不在乎是否以即时模式完成；实际上，我几乎会更喜欢。这是我要寻找的视觉输出：
佐尔科
看起来您有六个组成平截头体的平面（顶部，底部，左侧，左侧，右侧，正面，背面），被描述为四个分量，平面的法向矢量以及沿该矢量的距原点的距离（xyzD）。
一种简单的方法：给定任意三个平面，您可以找到带有一系列点和叉积的相关角点（因此，上，左，后为左上角-左后角；等等）。一个很好的参考是MonoGame.BoundingFrustum.IntersectionPoint方法（MIT许可证），该方法（在最近的优化之前）是：
Vector3 IntersectionPoint(ref Plane a, ref Plane b, ref Plane c)
{
// Formula used
// d1 ( N2 * N3 ) + d2 ( N3 * N1 ) + d3 ( N1 * N2 )
//P = ---------------------------------------------------------------------
// N1 . ( N2 * N3 )
//
// Note: N refers to the normal, d refers to the displacement. '.' means dot product. '*' means cross product
Vector3 v1, v2, v3;
float f = -Vector3.Dot(a.Normal, Vector3.Cross(b.Normal, c.Normal));
v1 = (a.D * (Vector3.Cross(b.Normal, c.Normal)));
v2 = (b.D * (Vector3.Cross(c.Normal, a.Normal)));
v3 = (c.D * (Vector3.Cross(a.Normal, b.Normal)));
Vector3 vec = new Vector3(v1.X + v2.X + v3.X, v1.Y + v2.Y + v3.Y, v1.Z + v2.Z + v3.Z);
return vec / f;
}
您可以对所有八个角重复此操作，然后将这些角连接在一起以将平截头体绘制为一系列线/边。
上面的链接是一个很好的参考-实际上，MonoGame代码及其XNA祖先都是“足够快”的几何处理的良好参考，并且MonoGame的MIT许可非常宽松。它们唯一的缺点往往是在坐标系惯用性，矩阵乘法顺序（行与列矩阵）等方面的假设。
我敢肯定，要获得完整图片，您需要使用其他相机查看结果，就像您提供的示例视觉输出一样。
本文收集自互联网，转载请注明来源。
如有侵权，请联系[email protected] 删除。
编辑于
相关文章
Related 相关文章
- 1
如何在netlogo中查看视锥
- 2
当相机位于视锥中时，OpenGL如何进行投影？
- 3
如何在OpenGL中绘制平截头体
- 4
如何在OpenGL中绘制平截头体
- 5
如何在OpenGL / C ++中绘制多维数据集？
- 6
如何在OpenGL中的单个绘制调用上绘制多个顶点数组？
- 7
如何使用MVP在OpenGL中绘制椭圆
- 8
如何在OpenGL中绘制一个立方体？
- 9
如何在OpenGL中创建网格并用线绘制它
- 10
如何在openGL c ++中的同一窗口中绘制两个对象？
- 11
如何在OpenGL着色器中从纹理图块贴图绘制图块？
- 12
如何在没有glBegin的情况下在OpenGL中绘制线
- 13
如何在 OpenGL C++ 中绘制多个三角形？
- 14
如何在（旧）opengl（2.4）中按程序绘制（超/n-）立方体
- 15
如何在OpenGL中加快在纹理上的绘制？（3.3 + / 4.1）
- 16
如何在 OpenGL 的立即模式下永久绘制东西？
- 17
在OpenGL中绘制像素
- 18
如何使用opengl在pyglet中批量绘制图元？
- 19
如何使用XCODE中的VBO使OpenGL绘制某些内容？
- 20
如何使用glew在Qt 5.7中绘制OpenGL几何
- 21
OpenGL视锥体教学法
- 22
如何在颤振中绘制或绘制全角矩形？
- 23
如何在SDL 2.0中绘制像素？
- 24
如何在R中绘制多个列？
- 25
如何在Firemonkey中绘制虚线？
- 26
如何在Matplotlib中绘制模糊点
- 27
如何在UILabel中绘制圆？
- 28
如何在熊猫中绘制多面图
- 29
如何在CSS中绘制圆扇形？
我来说两句