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This chapter is from the book

Texture Coordinate Generation

In Chapter 8, you learned that textures are mapped to geometry using texture coordinates. Often, when you are loading models (see Chapter 11, "It's All About the Pipeline: Faster Geometry Throughput"), texture coordinates are provided for you. If necessary, you can easily map texture coordinates manually to some surfaces such as spheres or flat planes. Sometimes, however, you may have a complex surface for which it is not so easy to manually derive the coordinates. OpenGL can automatically generate texture coordinates for you within certain limitations.

Texture coordinate generation is enabled on the S, T, R, and Q texture coordinates using glEnable:

glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glEnable(GL_TEXTURE_GEN_Q);

When texture coordinate generation is enabled, any calls to glTexCoord are ignored, and OpenGL calculates the texture coordinates for each vertex for you. In the same manner that texture coordinate generation is turned on, you turn it off by using glDisable:

glDisable(GL_TEXTURE_GEN_S);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_GEN_Q);

You set the function or method used to generate texture coordinates with the following functions:

void glTexGenf(GLenum coord, GLenum pname, GLfloat param);
void glTexGenfv(GLenum coord, GLenum pname, GLfloat *param);

The first parameter, coord, specifies which texture coordinate this function sets. It must be GL_S, GL_T, GL_R, or GL_Q. The second parameter, pname, must be GL_TEXTURE_GEN_MODE, GL_OBJECT_PLANE, or GL_EYE_PLANE. The last parameter sets the values of the texture generation function or mode. Note that integer (GLint) and double (GLdouble) versions of these functions are also used.

The pertinent portions of the sample program TEXGEN are presented in Listing 9.1. This program displays a torus that can be manipulated (rotated around) using the arrow keys. A right-click brings up a context menu that allows you to select from the first three texture generation modes we will discuss: Object Linear, Eye Linear, and Sphere Mapping.

Listing 9.1. Source Code for the TEXGEN Sample Program

#include "../../shared/gltools.h"   // gltools library

// Rotation amounts
static GLfloat xRot = 0.0f;
static GLfloat yRot = 0.0f;

GLuint toTextures[2];       // Two texture objects
int iRenderMode = 3;        // Sphere Mapped is default

///////////////////////////////////////////////////////////////////////////////
// Reset flags as appropriate in response to menu selections
void ProcessMenu(int value)
    {
    // Projection plane
    GLfloat zPlane[] = { 0.0f, 0.0f, 1.0f, 0.0f };

    // Store render mode
    iRenderMode = value;

    // Set up textgen based on menu selection
    switch(value)
        {
        case 1:
            // Object Linear
            glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
            glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
            glTexGenfv(GL_S, GL_OBJECT_PLANE, zPlane);
            glTexGenfv(GL_T, GL_OBJECT_PLANE, zPlane);
            break;

        case 2:
            // Eye Linear
            glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR);
            glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR);
            glTexGenfv(GL_S, GL_EYE_PLANE, zPlane);
            glTexGenfv(GL_T, GL_EYE_PLANE, zPlane);
            break;

        case 3:
        default:
            // Sphere Map
            glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);
            glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);
            break;
        }

    glutPostRedisplay();    // Redisplay
    }

///////////////////////////////////////////////////////////////////////////////
// Called to draw scene
void RenderScene(void)
    {
    // Clear the window with current clearing color
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    // Switch to orthographic view for background drawing
    glMatrixMode(GL_PROJECTION);
    glPushMatrix();
    glLoadIdentity();
    gluOrtho2D(0.0f, 1.0f, 0.0f, 1.0f);

    glMatrixMode(GL_MODELVIEW);
    glBindTexture(GL_TEXTURE_2D, toTextures[1]);    // Background texture

    // We will specify texture coordinates
    glDisable(GL_TEXTURE_GEN_S);
    glDisable(GL_TEXTURE_GEN_T);

    // No depth buffer writes for background
    glDepthMask(GL_FALSE);

    // Background image
    glBegin(GL_QUADS);
        glTexCoord2f(0.0f, 0.0f);
        glVertex2f(0.0f, 0.0f);

        glTexCoord2f(1.0f, 0.0f);
        glVertex2f(1.0f, 0.0f);

        glTexCoord2f(1.0f, 1.0f);
        glVertex2f(1.0f, 1.0f);

        glTexCoord2f(0.0f, 1.0f);
        glVertex2f(0.0f, 1.0f);
    glEnd();

    // Back to 3D land
    glMatrixMode(GL_PROJECTION);
    glPopMatrix();
    glMatrixMode(GL_MODELVIEW);

    // Turn texgen and depth writing back on
    glEnable(GL_TEXTURE_GEN_S);
    glEnable(GL_TEXTURE_GEN_T);
    glDepthMask(GL_TRUE);

    // May need to switch to stripe texture
    if(iRenderMode != 3)
        glBindTexture(GL_TEXTURE_2D, toTextures[0]);

    // Save the matrix state and do the rotations
    glPushMatrix();
    glTranslatef(0.0f, 0.0f, -2.0f);
    glRotatef(xRot, 1.0f, 0.0f, 0.0f);
    glRotatef(yRot, 0.0f, 1.0f, 0.0f);

    // Draw the tours
    gltDrawTorus(0.35, 0.15, 61, 37);

    // Restore the matrix state
    glPopMatrix();

    // Display the results
    glutSwapBuffers();
    }

Object Linear Mapping

When the texture generation mode is set to GL_OBJECT_LINEAR, texture coordinates are generated using the following function:

coord = P1*X + P2*Y + P3*Z + P4*W

The X, Y, Z, and W values are the vertex coordinates from the object being textured, and the P1–P4 values are the coefficients for a plane equation. The texture coordinates are then projected onto the geometry from the perspective of this plane. For example, to project texture coordinates for S and T from the plane Z = 0, we would use the following code from the TEXGEN sample program:

// Projection plane
GLfloat zPlane[] = { 0.0f, 0.0f, 1.0f, 0.0f };
. . .
. . .
// Object Linear
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_OBJECT_LINEAR);
glTexGenfv(GL_S, GL_OBJECT_PLANE, zPlane);
glTexGenfv(GL_T, GL_OBJECT_PLANE, zPlane);

Note that the texture coordinate generation function can be based on a different plane equation for each coordinate. Here, we simply use the same one for both the S and the T coordinates.

This technique maps the texture to the object in object coordinates, regardless of any modelview transformation in effect. Figure 9.7 shows the output for TEXGEN when the Object Linear mode is selected. No matter how you reorient the torus, the mapping remains fixed to the geometry.

Figure 9.7

Figure 9.7 Torus mapped with object linear coordinates.

Eye Linear Mapping

When the texture generation mode is set to GL_EYE_LINEAR, texture coordinates are generated in a similar manner to GL_OBJECT_LINEAR. The coordinate generation looks the same, except that now the X, Y, Z, and W coordinates indicate the location of the point of view (where the camera or eye is located). The plane equation coefficients are also inverted before being applied to the equation to account for the fact that now everything is in eye coordinates.

The texture, therefore, is basically projected from the plane onto the geometry. As the geometry is transformed by the modelview matrix, the texture will appear to slide across the surface. We set up this capability with the following code from the TEXGEN sample program:

// Projection plane
GLfloat zPlane[] = { 0.0f, 0.0f, 1.0f, 0.0f };
. . .
. . .
// Eye Linear
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR);
glTexGenfv(GL_S, GL_EYE_PLANE, zPlane);
glTexGenfv(GL_T, GL_EYE_PLANE, zPlane);

The output of the TEXGEN program when the Eye Linear menu option is selected is shown in Figure 9.8. As you move the torus around with the arrow keys, note how the projected texture slides about on the geometry.

Figure 9.8

Figure 9.8 An example of eye linear texture mapping.

Sphere Mapping

When the texture generation mode is set to GL_SPHERE_MAP, OpenGL calculates texture coordinates in such a way that the object appears to be reflecting the current texture map. This is the easiest mode to set up, with just these two lines from the TEXGEN sample program:

glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP);

You usually can make a well-constructed texture by taking a photograph through a fish-eye lens. This texture then lends a convincing reflective quality to the geometry. For more realistic results, sphere mapping has largely been replaced by cube mapping (discussed next). However, sphere mapping still has some uses because it has significantly less overhead.

In particular, sphere mapping requires only a single texture instead of six, and if true reflectivity is not required, you can obtain adequate results from sphere mapping. Even without a well-formed texture taken through a fish-eye lens, you can also use sphere mapping for an approximate environment map. Many surfaces are shiny and reflect the light from their surroundings, but are not mirror-like in their reflective qualities. In the TEXGEN sample program, we use a suitable environment map for the background (all modes show this background), as well as the source for the sphere map. Figure 9.9 shows the environment-mapped torus against a similarly colored background. Moving the torus around with the arrow keys produces a reasonable approximation of a reflective surface.

Figure 9.9

Figure 9.9 An environment map using a sphere map.

Cube Mapping

The last two texture generation modes, GL_REFLECTION_MAP and GL_NORMAL_MAP, require the use of a new type of texture target: the cube map. A cube map is treated as a single texture, but is made up of six square (yes, they must be square!) 2D images that make up the six sides of a cube. Figure 9.10 shows the layout of six square textures composing a cube map for the CUBEMAP sample program.

Figure 9.10

Figure 9.10 The layout of six cube faces in the CUBEMAP sample program.

These six 2D tiles represent the view of the world from six different directions (negative and positive X, Y, and Z). Using the texture generation mode GL_REFLECTION_MAP, you can then create a realistically reflective surface.

Loading Cube Maps

Cube maps add six new values that can be passed into glTexImage2D: GL_TEXTURE_CUBE_MAP_POSITIVE_X, GL_TEXTURE_CUBE_MAP_NEGATIVE_X, GL_TEXTURE_CUBE_MAP_POSITIVE_Y, GL_TEXTURE_CUBE_MAP_NEGATIVE_Y, GL_TEXTURE_CUBE_MAP_POSITIVE_Z, and GL_TEXTURE_CUBE_MAP_NEGATIVE_Z. These constants represent the direction in world coordinates of the cube face surrounding the object being mapped. For example, to load the map for the positive X direction, you might use a function that looks like this:

glTexImage2D(GL_TEXTURE_CUBE_MAP_POSITIVE_X, 0, GL_RGBA, iWidth, iHeight,
                                        0, GL_RGBA, GL_UNSIGNED_BYTE, pImage);

To take this example further, look at the following code segment from the CUBEMAP sample program. Here, we store the name and identifiers of the six cube maps in arrays and then use a loop to load all six images into a single texture object:

const char *szCubeFaces[6] = { "pos_x.tga", "neg_x.tga", "pos_y.tga",
                     "neg_y.tga","pos_z.tga", "neg_z.tga" };

GLenum cube[6] = {  GL_TEXTURE_CUBE_MAP_POSITIVE_X,
                    GL_TEXTURE_CUBE_MAP_NEGATIVE_X,
                    GL_TEXTURE_CUBE_MAP_POSITIVE_Y,
                    GL_TEXTURE_CUBE_MAP_NEGATIVE_Y,
                    GL_TEXTURE_CUBE_MAP_POSITIVE_Z,
                    GL_TEXTURE_CUBE_MAP_NEGATIVE_Z };

. . .
. . .

    glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
    glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_TEXTURE_MIN_FILTER,
                                                  GL_LINEAR_MIPMAP_LINEAR);
    glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
    glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
    glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);

    GLbyte *pBytes;
    GLint iWidth, iHeight, iComponents;
    GLenum eFormat;

    // Load Cube Map images
    for(i = 0; i < 6; i++)
        {
        // Load this texture map
        glTexParameteri(GL_TEXTURE_CUBE_MAP, GL_GENERATE_MIPMAP, GL_TRUE);
        pBytes = gltLoadTGA(szCubeFaces[i], &iWidth, &iHeight,
                                                      &iComponents, &eFormat);
        glTexImage2D(cube[i], 0, iComponents, iWidth, iHeight, 0, eFormat,
                                                    GL_UNSIGNED_BYTE, pBytes);
        free(pBytes);
        }

To enable the application of the cube map, we now call glEnable with GL_TEXTURE_CUBE_MAP instead of GL_TEXTURE_2D (we also use the same value in glBindTexture when using texture objects):

glEnable(GL_TEXTURE_CUBE_MAP);

If both GL_TEXTURE_CUBE_MAP and GL_TEXTURE_2D are enabled, GL_TEXTURE_CUBE_MAP has precedence. Also, notice that the texture parameter values (set with glTexParameter) affect all six images in a single cube texture.

Texture coordinates for cube maps seem a little odd at first glance. Unlike a true 3D texture, the S, T, and R texture coordinates represent a signed vector from the center of the texture map. This vector intersects one of the six sides of the cube map. The texels around this intersection point are then sampled to create the filtered color value from the texture.

Using Cube Maps

The most common use of cube maps is to create an object that reflects its surroundings. The six images used for the CUBEMAP sample program were provided courtesy of The Game Creators, Ltd. (www.thegamecreators.com). This cube map is applied to a sphere, creating the appearance of a mirrored surface. This same cube map is also applied to the skybox, which creates the background being reflected.

A skybox is nothing more than a big box with a picture of the sky on it. Another way of looking at it is as a picture of the sky on a big box! Simple enough. An effective skybox contains six images that contain views from the center of your scene along the six directional axes. If this sounds just like a cube map, congratulations, you're paying attention! For our CUBEMAP sample program a large box is drawn around the scene, and the CUBEMAP texture is applied to the six faces of the cube. The skybox is drawn as a single batch of six GL_QUADS. Each face is then manually textured using glTexCoord3f. For each vertex, a vector is specified that points to that corner of the sky box. The first side (in the negative X direction) is shown here:

glBegin(GL_QUADS);
        //////////////////////////////////////////////
        // Negative X
        glTexCoord3f(-1.0f, -1.0f, 1.0f);
        glVertex3f(-fExtent, -fExtent, fExtent);

        glTexCoord3f(-1.0f, -1.0f, -1.0f);
        glVertex3f(-fExtent, -fExtent, -fExtent);

        glTexCoord3f(-1.0f, 1.0f, -1.0f);
        glVertex3f(-fExtent, fExtent, -fExtent);

        glTexCoord3f(-1.0f, 1.0f, 1.0f);
        glVertex3f(-fExtent, fExtent, fExtent);

. . .
. . .

It is important to remember that in order for the manual selection of texture coordinates via glTexCoord3f to work, you must disable the texture coordinate generation:

// Sky Box is manually textured
glDisable(GL_TEXTURE_GEN_S);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_R);
DrawSkyBox();

To draw the reflective sphere, the CUBEMAP sample sets the texture generation mode to GL_REFLECTION_MAP for all three texture coordinates:

glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP);
glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP);
glTexGeni(GL_R, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP);

We must also make sure that texture coordinate generation is enabled:

// Use texgen to apply cube map
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);

To provide a true reflection, we also take the orientation of the camera into account. The camera's rotation matrix is extracted from the camera class, and inverted. This is then applied to the texture matrix before the cube map is applied. Without this rotation of the texture coordinates, the cube map will not correctly reflect the surrounding skybox. Since the gltDrawSphere function makes no modelview matrix mode changes, we can also leave the matrix mode as GL_TEXTURE until we are through drawing and have restored the texture matrix to its original state (usually this will be the identity matrix):

glMatrixMode(GL_TEXTURE);
    glPushMatrix();

    // Invert camera matrix (rotation only) and apply to
    // texture coordinates
    M3DMatrix44f m, invert;
    frameCamera.GetCameraOrientation(m);
    m3dInvertMatrix44(invert, m);
    glMultMatrixf(invert);

     gltDrawSphere(0.75f, 41, 41);

     glPopMatrix();
glMatrixMode(GL_MODELVIEW);

Figure 9.11 shows the output of the CUBEMAP sample program. Notice how the sky and surrounding terrain are reflected correctly off the surface of the sphere. Moving the camera around the sphere (by using the arrow keys) reveals the correct background and sky view reflected accurately off the sphere as well.

Figure 9.11

Figure 9.11 Output from the CUBEMAP sample program. (This figure also appears in the Color insert.)

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