纹理投影流程
cg toolkit中关于纹理投影的例子
一 主程序中执行的空间变换
二 shader执行的render pipe处理
1 建立视点矩阵
eyePosition[3];//观察视点位置
lightPosition[3];//光源位置,或投影视点位置
center[3];//投影中心,是地形或模型上的一点
up[3];上向量方向,一般为Y轴正方向
buildLookAtMatrix(eyePosition[0], eyePosition[1], eyePosition[2],
center[0], center[1], center[2],
up[0], up[1], up[2],
eyeViewMatrix);
buildLookAtMatrix(lightPosition[0], lightPosition[1], lightPosition[2],
center[0], center[1], center[2],
up[0], -up[1], up[2], /* Flip up for projected texture's view */
lightViewMatrix);
//buildLookAtMatrix实现
View Code
/* Build a row-major (C-style) 4x4 matrix transform based on the
parameters for gluLookAt. */
static void buildLookAtMatrix(double eyex, double eyey, double eyez,
double centerx, double centery, double centerz,
double upx, double upy, double upz,
float m[16])
{
double x[3], y[3], z[3], mag;
/* Difference eye and center vectors to make Z vector. */
z[0] = eyex - centerx;
z[1] = eyey - centery;
z[2] = eyez - centerz;
/* Normalize Z. */
mag = sqrt(z[0]*z[0] + z[1]*z[1] + z[2]*z[2]);
if (mag) {
z[0] /= mag;
z[1] /= mag;
z[2] /= mag;
}
/* Up vector makes Y vector. */
y[0] = upx;
y[1] = upy;
y[2] = upz;
/* X vector = Y cross Z. */
x[0] = y[1]*z[2] - y[2]*z[1];
x[1] = -y[0]*z[2] + y[2]*z[0];
x[2] = y[0]*z[1] - y[1]*z[0];
/* Recompute Y = Z cross X. */
y[0] = z[1]*x[2] - z[2]*x[1];
y[1] = -z[0]*x[2] + z[2]*x[0];
y[2] = z[0]*x[1] - z[1]*x[0];
/* Normalize X. */
mag = sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
if (mag) {
x[0] /= mag;
x[1] /= mag;
x[2] /= mag;
}
/* Normalize Y. */
mag = sqrt(y[0]*y[0] + y[1]*y[1] + y[2]*y[2]);
if (mag) {
y[0] /= mag;
y[1] /= mag;
y[2] /= mag;
}
/* Build resulting view matrix. */
m[0*4+0] = x[0]; m[0*4+1] = x[1];
m[0*4+2] = x[2]; m[0*4+3] = -x[0]*eyex + -x[1]*eyey + -x[2]*eyez;
m[1*4+0] = y[0]; m[1*4+1] = y[1];
m[1*4+2] = y[2]; m[1*4+3] = -y[0]*eyex + -y[1]*eyey + -y[2]*eyez;
m[2*4+0] = z[0]; m[2*4+1] = z[1];
m[2*4+2] = z[2]; m[2*4+3] = -z[0]*eyex + -z[1]*eyey + -z[2]*eyez;
m[3*4+0] = 0.0; m[3*4+1] = 0.0; m[3*4+2] = 0.0; m[3*4+3] = 1.0;
}
2 创建模型矩阵modelMatrix
/* modelView = rotateMatrix * translateMatrix */
makeRotateMatrix(70, 1, 1, 1, rotateMatrix);
makeTranslateMatrix(2, 0, 0, translateMatrix);
multMatrix(modelMatrix, translateMatrix, rotateMatrix);
Opengl中设置模型方位和位置.Ogre中自己获取参数.该矩阵即model到世界空间的变换矩阵.
//makeRotateMatrix实现
View Code
/* Build a row-major (C-style) 4x4 matrix transform based on the
parameters for glRotatef. */
static void makeRotateMatrix(float angle,
float ax, float ay, float az,
float m[16])
{
float radians, sine, cosine, ab, bc, ca, tx, ty, tz;
float axis[3];
axis[0] = ax;
axis[1] = ay;
axis[2] = az;
normalizeVector(axis);
radians = angle * myPi / 180.0;
sine = sin(radians);
cosine = cos(radians);
ab = axis[0] * axis[1] * (1 - cosine);
bc = axis[1] * axis[2] * (1 - cosine);
ca = axis[2] * axis[0] * (1 - cosine);
tx = axis[0] * axis[0];
ty = axis[1] * axis[1];
tz = axis[2] * axis[2];
m[0] = tx + cosine * (1 - tx);
m[1] = ab + axis[2] * sine;
m[2] = ca - axis[1] * sine;
m[3] = 0.0f;
m[4] = ab - axis[2] * sine;
m[5] = ty + cosine * (1 - ty);
m[6] = bc + axis[0] * sine;
m[7] = 0.0f;
m[8] = ca + axis[1] * sine;
m[9] = bc - axis[0] * sine;
m[10] = tz + cosine * (1 - tz);
m[11] = 0;
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1;
}
//makeTranslateMatrix实现
View Code
/* Build a row-major (C-style) 4x4 matrix transform based on the
parameters for glTranslatef. */
static void makeTranslateMatrix(float x, float y, float z, float m[16])
{
m[0] = 1; m[1] = 0; m[2] = 0; m[3] = x;
m[4] = 0; m[5] = 1; m[6] = 0; m[7] = y;
m[8] = 0; m[9] = 0; m[10] = 1; m[11] = z;
m[12] = 0; m[13] = 0; m[14] = 0; m[15] = 1;
}
//multMatrix实现
View Code
/* Simple 4x4 matrix by 4x4 matrix multiply. */
static void multMatrix(float dst[16],
const float src1[16], const float src2[16])
{
float tmp[16];
int i, j;
for (i=0; i<4; i++) {
for (j=0; j<4; j++) {
tmp[i*4+j] = src1[i*4+0] * src2[0*4+j] +
src1[i*4+1] * src2[1*4+j] +
src1[i*4+2] * src2[2*4+j] +
src1[i*4+3] * src2[3*4+j];
}
}
/* Copy result to dst (so dst can also be src1 or src2). */
for (i=0; i<16; i++)
dst[i] = tmp[i];
}
3 建立光源到model空间的变换矩阵
/* invModelMatrix = inverse(modelMatrix) */
invertMatrix(invModelMatrix, modelMatrix);
/* Transform world-space light positions to sphere's object-space. */
transform(objSpaceLightPosition, invModelMatrix, lightPosition);
cgSetParameter3fv(myCgVertexParam_lightPosition, objSpaceLightPosition);
实际上既是求modelMatrix的逆矩阵.然后将光源位置(或投影视点)转换到model空间.
//invertMatrix
View Code
/* Invert a row-major (C-style) 4x4 matrix. */
static void invertMatrix(float *out, const float *m)
{
/* Assumes matrices are ROW major. */
#define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(r)*4+(c)]
double wtmp[4][8];
double m0, m1, m2, m3, s;
double *r0, *r1, *r2, *r3;
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
/* Choose myPivot, or die. */
if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
if (0.0 == r0[0]) {
assert(!"could not invert matrix");
}
/* Eliminate first variable. */
m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
s = r0[4];
if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
s = r0[5];
if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
s = r0[6];
if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
s = r0[7];
if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
/* Choose myPivot, or die. */
if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
if (0.0 == r1[1]) {
assert(!"could not invert matrix");
}
//transform实现
View Code
/* Simple 4x4 matrix by 4-component column vector multiply. */
static void transform(float dst[4],
const float mat[16], const float vec[4])
{
double tmp[4], invW;
int i;
for (i=0; i<4; i++) {
tmp[i] = mat[i*4+0] * vec[0] +
mat[i*4+1] * vec[1] +
mat[i*4+2] * vec[2] +
mat[i*4+3] * vec[3];
}
invW = 1 / tmp[3];
/* Apply perspective divide and copy to dst (so dst can vec). */
for (i=0; i<3; i++)
dst[i] = tmp[i] * invW;
dst[3] = 1;
}
4 创建模型视点矩阵
/* modelViewMatrix = eyeViewMatrix * modelMatrix */
multMatrix(modelViewMatrix, eyeViewMatrix, modelMatrix);
model到视点空间的变换矩阵.
5 创建模型视点投影矩阵
/* modelViewProj = projectionMatrix * modelViewMatrix */
multMatrix(modelViewProjMatrix, projectionMatrix, modelViewMatrix);
projectionMatrix根据以下参数确定:视点空间变换到投影空间的变换矩阵.该步骤与纹理投影无关.
fieldOfView(FOV):视角大小;
aspectRatio(aspect):长宽比
zNear(near):近裁剪面
zFar(far):远裁剪面
//buildPerspectiveMatrix实现
View Code
/* Build a row-major (C-style) 4x4 matrix transform based on the
parameters for gluPerspective. */
static void buildPerspectiveMatrix(double fieldOfView,
double aspectRatio,
double zNear, double zFar,
float m[16])
{
double sine, cotangent, deltaZ;
double radians = fieldOfView / 2.0 * myPi / 180.0;
deltaZ = zFar - zNear;
sine = sin(radians);
/* Should be non-zero to avoid division by zero. */
assert(deltaZ);
assert(sine);
assert(aspectRatio);
cotangent = cos(radians) / sine;
m[0*4+0] = cotangent / aspectRatio;
m[0*4+1] = 0.0;
m[0*4+2] = 0.0;
m[0*4+3] = 0.0;
m[1*4+0] = 0.0;
m[1*4+1] = cotangent;
m[1*4+2] = 0.0;
m[1*4+3] = 0.0;
m[2*4+0] = 0.0;
m[2*4+1] = 0.0;
m[2*4+2] = -(zFar + zNear) / deltaZ;
m[2*4+3] = -2 * zNear * zFar / deltaZ;
m[3*4+0] = 0.0;
m[3*4+1] = 0.0;
m[3*4+2] = -1;
m[3*4+3] = 0;
}
6 创建纹理投影矩阵
buildTextureMatrix(lightViewMatrix, modelMatrix, /*out*/textureMatrix);
/* Set matrix parameter with row-major matrix. */
cgSetMatrixParameterfr(myCgVertexParam_modelViewProj, modelViewProjMatrix);
cgSetMatrixParameterfr(myCgVertexParam_textureMatrix, textureMatrix);
static void buildTextureMatrix(const float viewMatrix[16],
const float modelMatrix[16],
float textureMatrix[16])
{
static float eyeToClipMatrix[16];
float modelViewMatrix[16];
static int needsInit = 1;
if (needsInit) {
const float fieldOfView = 50.0f;
const float aspectRatio = 1;
float textureProjectionMatrix[16];
float clipToTextureMatrix[16];
/* Build texture projection matrix once. */
buildPerspectiveMatrix(fieldOfView, aspectRatio,
0.25, 20.0, /* Znear and Zfar */
textureProjectionMatrix);
makeClipToTextureMatrix(clipToTextureMatrix);
/* eyeToClip = clipToTexture * textureProjection */
multMatrix(eyeToClipMatrix,
clipToTextureMatrix, textureProjectionMatrix);
needsInit = 1;
}
/* modelView = view * model */
multMatrix(modelViewMatrix, viewMatrix, modelMatrix);
/* texture = eyeToClip * modelView */
multMatrix(textureMatrix, eyeToClipMatrix, modelViewMatrix);
}
该函数中:
1> buildPerspectiveMatrix同前面的,不过这里用来计算用于投影纹理的视景体变换(投影变换).
2> makeClipToTextureMatrix(clipToTextureMatrix)建立视景体裁切矩阵.
因为视景体是长度为1的单位空间.
3> 将1, 2步的矩阵相乘: multMatrix(eyeToClipMatrix,clipToTextureMatrix,textureProjectionMatrix);
eyeToClipMatrix为得到的纹理投影裁剪变换矩阵.
4> multMatrix(modelViewMatrix, viewMatrix, modelMatrix);
modelViewMatrix为从模型空间到光源(投影视点)空间的变换矩阵.
5> 将3, 4步的结果相乘:
multMatrix(textureMatrix, eyeToClipMatrix, modelViewMatrix);
textureMatrix为从模型视点空间(基于光源位置或投影视点)到纹理投影裁剪空间的变换矩阵.
textureMatrix此即最终的纹理投影变换矩阵.从这些流程可以明白,实际上是把模型投影到纹理上.
顶点程序:
void C9E5v_projTex(float4 position : POSITION,
float3 normal : NORMAL,
out float4 oPosition : POSITION,
out float4 texCoordProj : TEXCOORD0,
out float4 diffuseLighting : COLOR,
uniform float Kd,
uniform float4x4 modelViewProj,
uniform float3 lightPosition,
uniform float4x4 textureMatrix)
{
oPosition = mul(modelViewProj, position);
// Compute texture coordinates for
// querying the projective texture
texCoordProj = mul(textureMatrix, position);
// Compute diffuse lighting
float3 N = normalize(normal);
float3 L = normalize(lightPosition - position.xyz);
diffuseLighting = Kd * max(dot(N, L), 0);
}
片段程序:
void C9E6f_projTex(float4 texCoordProj : TEXCOORD0,
float4 diffuseLighting : COLOR,
out float4 color : COLOR,
uniform sampler2D projectiveMap)
{
// Fetch color from the projective texture
float4 textureColor = tex2Dproj(projectiveMap,
texCoordProj);
color = textureColor * diffuseLighting;
}
