地形高度算法小结

地形一般是用网格再从高度图里读取每个顶点的高度来生成。若进一步，想实现摄像机在地形上行走的效果，就需要算出地形上任意一点的高度。总结了3个方法：

 

一：

《Introduction to 3D Game Programming With Directx 9.0》这本书里介绍的，利用向量来算。

 

float Terrain::GetHeight(float x, float z)
{
  // Translate on xz-plane by the transformation that takes
 // the terrain START point to the origin.
 x = ((float)_width / 2.0f) + x;
 z = ((float)_depth / 2.0f) - z;

 // Scale down by the transformation that makes the
 // cellspacing equal to one.  This is given by
 // 1 / cellspacing since; cellspacing * 1 / cellspacing = 1.
 x /= (float)_CellSpacing;
 z /= (float)_CellSpacing;

 // From now on, we will interpret our positive z-axis as
 // going in the 'down' direction, rather than the 'up' direction.
 // This allows to extract the row and column simply by 'flooring'
 // x and z:

 float col = ::floorf(x);
 float row = ::floorf(z);

 // get the heights of the quad we're in:
 //
    //  A   B
    //  *---*
    //    | / |
    //  *---* 
    //  C   D

 float A = GetHeightMapEntry(row,   col);
 float B = GetHeightMapEntry(row,   col+1);
 float C = GetHeightMapEntry(row+1, col);
 float D = GetHeightMapEntry(row+1, col+1);

 //
 // Find the triangle we are in:
 //

 // Translate by the transformation that takes the upper-left
 // corner of the cell we are in to the origin.  Recall that our
 // cellspacing was nomalized to 1.  Thus we have a unit square
 // at the origin of our +x -> 'right' and +z -> 'down' system.
 float dx = x - col;
 float dz = z - row;

 // Note the below compuations of u and v are unneccessary, we really
 // only need the height, but we compute the entire vector to emphasis
 // the books discussion.
 float height = 0.0f;
 if(dz < 1.0f - dx)  // upper triangle ABC
 {
  float uy = B - A; // A->B
  float vy = C - A; // A->C

  // Linearly interpolate on each vector.  The height is the vertex
  // height the vectors u and v originate from {A}, plus the heights
  // found by interpolating on each vector u and v.
  height = A + Lerp(0.0f, uy, dx) + Lerp(0.0f, vy, dz);
 }
 else // lower triangle DCB
 {
  float uy = C - D; // D->C
  float vy = B - D; // D->B

  // Linearly interpolate on each vector.  The height is the vertex
  // height the vectors u and v originate from {D}, plus the heights
  // found by interpolating on each vector u and v.
  height = D + Lerp(0.0f, uy, 1.0f - dx) + Lerp(0.0f, vy, 1.0f - dz);
 }

 return height;
}

 

用到的2个函数

float Terrain::Lerp(float a, float b, float t)     //一个插值函数
{
 return (a - (a*t) + (b*t));
}

 

int Terrain::GetHeightMapEntry(int row, int col)         //读取高度函数
{
 return _heightmap[row * _numVertsPerRow + col];   // 高度图数据存在_heightmap里
}

 

二：

先计算出摄像机所在三角形的平面方程，然后带入摄像机的X，Z坐标，即可得高度Y

具体实现过程见 [url]http://creatorchen1984.spaces.live.com/[/url] 《获取地形上某一点高度》，写的十分详细

 

三：

网上找的一个方法

假设你的地形为terrain[][];用下面的函数求出地形上点(x,z);的y值,将人物的高度加上这个y值即可.
float GetHeight(GLfloat x, GLfloat z)
{
float h=0;
float Xb,Yb;
int Xa,Ya;
Xa=(int)x;
Ya=(int)z;
Xb=x-Xa;
Yb=z-Ya;

float a=terrain[Xa][Ya].y;
float b=terrain[Xa+1][Ya].y;
float c=terrain[Xa][Ya+1].y;
float d=terrain[Xa+1][Ya+1].y;
h=(a*(1-Xb)+b*Xb)*(1-Yb)+(c*(1-Xb)+d*Xb)*Yb;
return h;
}