如何在OpenGL中绘制一个Frustum
我使用C＃和OpenTK创建了一个平截头体课程，它完美无缺。但是，我希望能够绘制平截头体的边界以进行调试。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该怎么做。
这是我的Frustum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.
}
}
}
有谁知道如何绘制Frustum？而且我不在乎它是否以立即模式完成;事实上，我几乎更喜欢这样。这是我正在寻找的视觉输出：
2 个答案:
答案 0 :(得分：4)
看起来你有六个平面组成平截头体（顶部，底部，左，右，前，后）描述为四个分量，平面的法向量和从原点开始沿着该向量的距离（xyzD）
一种简单的方法：给定任意三个平面，您可以找到相关的角点（左上角，左上角，后左上角等等），带有一系列点和十字产品。一个很好的参考是MonoGame.BoundingFrustum.IntersectionPoint方法（麻省理工学院许可证），它（在最近的优化之前）：
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，然后将角连接在一起以将平截头体绘制为一系列线条/边。
以上链接是一个相当不错的参考 - 实际上MonoGame代码及其XNA祖先都是几何处理的良好参考，足够快＆＃34;以及MonoGame的MIT许可证是very permissive。它们唯一的缺点往往是坐标系统手性，矩阵乘法次序（行与列矩阵）之类的假设等。
我确定不言而喻，为了获得完整的图片，您想要使用不同的相机查看结果，就像您提供的样本视觉输出一样。
答案 1 :(得分：3)
这些建议都不是你所要求的，但它们可能会帮助你思考它。
尽可能接近（假设代码有效，正如你所说的那样），_frustum数组定义了截锥体两侧的6个平面。
因此，您可以通过计算相应平面的交点来简单地计算体积拐角处的8个点（如下所述：Point of intersection of three planes 3D - C#）
我怀疑当你计算出方程式时，它们会根据clipmatrix中的数据简化为一些相对简单的表达式。
或者，如果您知道您的perspectivematrix定义的平截头体（在相对于视点的简单规范坐标中，沿z轴居中），您可以简单地反转modelViewMatrix并将这些点乘以它，为您提供点数回到世界坐标。
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