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。
1 
float Terrain::GetHeight( float x, float z)
2
{
3
// Translate on xz-plane by the transformation that takes
4 // the terrain START point to the origin.
5 x = (( float )_width / 2.0f ) + x;
6 z = (( float )_depth / 2.0f ) - z;
7 // Scale down by the transformation that makes the
8 // cellspacing equal to one. This is given by
9 // 1 / cellspacing since; cellspacing * 1 / cellspacing = 1.
10 x /= ( float )_CellSpacing;
11 z /= ( float )_CellSpacing;
12 // From now on, we will interpret our positive z-axis as
13 // going in the 'down' direction, rather than the 'up' direction.
14 // This allows to extract the row and column simply by 'flooring'
15 // x and z:
16 float col = ::floorf(x);
17 float row = ::floorf(z);
18 // get the heights of the quad we're in:
19 //
20 // A B
21 // *---*
22 // | / |
23 // *---*
24 // C D
25 float A = GetHeightMapEntry(row, col);
26 float B = GetHeightMapEntry(row, col + 1 );
27 float C = GetHeightMapEntry(row + 1 , col);
28 float D = GetHeightMapEntry(row + 1 , col + 1 );
29 //
30 // Find the triangle we are in:
31 //
32 // Translate by the transformation that takes the upper-left
33 // corner of the cell we are in to the origin. Recall that our
34 // cellspacing was nomalized to 1. Thus we have a unit square
35 // at the origin of our +x -> 'right' and +z -> 'down' system.
36 float dx = x - col;
37 float dz = z - row;
38 // Note the below compuations of u and v are unneccessary, we really
39 // only need the height, but we compute the entire vector to emphasis
40 // the books discussion.
41 float height = 0.0f ;
42 if (dz < 1.0f - dx) // upper triangle ABC
43
{
44 float uy = B - A; // A->B
45 float vy = C - A; // A->C
46 // Linearly interpolate on each vector. The height is the vertex
47 // height the vectors u and v originate from {A}, plus the heights
48 // found by interpolating on each vector u and v.
49 height = A + Lerp( 0.0f , uy, dx) + Lerp( 0.0f , vy, dz);
50
}
51 else // lower triangle DCB
52 {
53 float uy = C - D; // D->C
54 float vy = B - D; // D->B
55 // Linearly interpolate on each vector. The height is the vertex
56 // height the vectors u and v originate from {D}, plus the heights
57 // found by interpolating on each vector u and v.
58 height = D + Lerp( 0.0f , uy, 1.0f - dx) + Lerp( 0.0f , vy, 1.0f - dz);
59 }
60 return height;
61
}
62
float Terrain::GetHeight( float x, float z)2
{
3
// Translate on xz-plane by the transformation that takes4
// the terrain START point to the origin. 5
x = (( float )_width / 2.0f ) + x;6
z = (( float )_depth / 2.0f ) - z;7
// Scale down by the transformation that makes the 8
// cellspacing equal to one. This is given by 9
// 1 / cellspacing since; cellspacing * 1 / cellspacing = 1. 10
x /= ( float )_CellSpacing;11
z /= ( float )_CellSpacing;12
// From now on, we will interpret our positive z-axis as13
// going in the 'down' direction, rather than the 'up' direction.14
// This allows to extract the row and column simply by 'flooring'15
// x and z: 16
float col = ::floorf(x);17
float row = ::floorf(z);18
// get the heights of the quad we're in:19
// 20
// A B21
// *---*22
// | / |23
// *---* 24
// C D 25
float A = GetHeightMapEntry(row, col);26
float B = GetHeightMapEntry(row, col + 1 );27
float C = GetHeightMapEntry(row + 1 , col);28
float D = GetHeightMapEntry(row + 1 , col + 1 );29
// 30
// Find the triangle we are in:31
// 32
// Translate by the transformation that takes the upper-left33
// corner of the cell we are in to the origin. Recall that our 34
// cellspacing was nomalized to 1. Thus we have a unit square35
// at the origin of our +x -> 'right' and +z -> 'down' system. 36
float dx = x - col;37
float dz = z - row;38
// Note the below compuations of u and v are unneccessary, we really39
// only need the height, but we compute the entire vector to emphasis40
// the books discussion. 41
float height = 0.0f ;42
if (dz < 1.0f - dx) // upper triangle ABC 43
{
44
float uy = B - A; // A->B 45
float vy = C - A; // A->C46
// Linearly interpolate on each vector. The height is the vertex47
// height the vectors u and v originate from {A}, plus the heights48
// found by interpolating on each vector u and v. 49
height = A + Lerp( 0.0f , uy, dx) + Lerp( 0.0f , vy, dz);50
} 51
else // lower triangle DCB 52
{53
float uy = C - D; // D->C 54
float vy = B - D; // D->B55
// Linearly interpolate on each vector. The height is the vertex56
// height the vectors u and v originate from {D}, plus the heights57
// found by interpolating on each vector u and v. 58
height = D + Lerp( 0.0f , uy, 1.0f - dx) + Lerp( 0.0f , vy, 1.0f - dz);59
} 60
return height;61
} 62
用到的2个函数
1float Terrain::Lerp(float a, float b, float t) //一个插值函数
2{
3 return (a - (a*t) + (b*t));
4}
5
6int Terrain::GetHeightMapEntry(int row, int col) //读取高度函数
7{
8 return _heightmap[row * _numVertsPerRow + col]; // 高度图数据存在_heightmap里
9}
float Terrain::Lerp(float a, float b, float t) //一个插值函数2
{3
return (a - (a*t) + (b*t));4
}5
6
int Terrain::GetHeightMapEntry(int row, int col) //读取高度函数7
{8
return _heightmap[row * _numVertsPerRow + col]; // 高度图数据存在_heightmap里9
}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http://creatorchen1984.spaces.live.com/ 《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.
1float GetHeight(GLfloat x, GLfloat z)
2{
3float h=0;
4float Xb,Yb;
5int Xa,Ya;
6Xa=(int)x;
7Ya=(int)z;
8Xb=x-Xa;
9Yb=z-Ya;
10float a=terrain[Xa][Ya].y;
11float b=terrain[Xa+1][Ya].y;
12float c=terrain[Xa][Ya+1].y;
13float d=terrain[Xa+1][Ya+1].y;
14h=(a*(1-Xb)+b*Xb)*(1-Yb)+(c*(1-Xb)+d*Xb)*Yb;
15return h;
16}
17
float GetHeight(GLfloat x, GLfloat z)2
{ 3
float h=0;4
float Xb,Yb;5
int Xa,Ya;6
Xa=(int)x;7
Ya=(int)z;8
Xb=x-Xa;9
Yb=z-Ya;10
float a=terrain[Xa][Ya].y;11
float b=terrain[Xa+1][Ya].y;12
float c=terrain[Xa][Ya+1].y;13
float d=terrain[Xa+1][Ya+1].y;14
h=(a*(1-Xb)+b*Xb)*(1-Yb)+(c*(1-Xb)+d*Xb)*Yb;15
return h;16
} 17
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