Texture and Environment Mapping

Texture Mapping and Environment Mapping

Cheap way to enhance object appearance: Textures provide a cost-effective method for making objects look more complex and detailed without increasing the number of vertices and edges.
Reduced computational cost: Using textures reduces the computational load compared to rendering highly detailed models.

Texture mapping involves applying a 2D image onto the surface of a 3D object.
Texture images are typically defined by coordinates S and T, which range from 0 to 1.
The surface of a 3D object is a 2D area residing in a 3D space (with X, Y, and Z coordinates).
The goal is to map texture elements (texels) to pixels on the screen.
Texels are the elements of a texture image.

Texture coordinates are represented as S and T, with values between 0 and 1.
The coordinates specify how the texture image is mapped onto the object's surface.

A sphere can be mapped with a 2D texture image by correlating points in 3D space to points on the texture.
3D points in space can be defined using polar angles:
- \theta (theta): the angle between the radius vector r and the z-axis.
- \phi (phi): the angle between the projection of r onto the xy-plane and the x-axis.

Given radius r, the Cartesian coordinates can be defined as:
- z = r \cos(\theta)
- x = r \sin(\theta) \cos(\phi)
- y = r \sin(\theta) \sin(\phi)

Establish a linear relationship between angles \theta and \phi and texture coordinates S and T.
\phi ranges from 0 to 2\pi, and \theta ranges from 0 to \pi.
The relationships are:
- S = \frac{\phi}{2\pi}
- T = \frac{\theta}{\pi}
To find the correlation between 3D points and 2D texture coordinates, extract \phi and \theta from x, y, and z:
- \theta = \arccos(\frac{z}{r})
- \phi = \arctan(\frac{y}{x})
  *Substituting these relations into the equations above, we have
- S = \frac{\arctan(\frac{y}{x})}{2\pi}
- T = \frac{\arccos(\frac{z}{r})}{\pi}

GL_REPEAT: Repeats the texture across the surface.
GLMIRROREDREPEAT: Mirrors the texture at integer boundaries, which is useful for textures with contrast changes to avoid visible seams.
GLCLAMPTO_EDGE: Clamps the texture coordinates to the edge, repeating the edge pixels.
GLCLAMPTO_BORDER: Assigns a default border color to coordinates outside the [0, 1] range.

Pelting: Unstitches and unfolds the 3D object's surface to create a 2D texture map; may introduce distortions for complex objects.
Fast Textures: Defines texture maps by patching local textures together, which is more computationally efficient.

Forward Mapping: Starts from the texture space, maps the texture onto the object, and then projects the object onto the screen.
Inverse Mapping: Starts from the screen space and determines which point in the texture image corresponds to each pixel.

Start with texture coordinates S and T.
Map S and T to the object's surface in 3D space using the sphere equations.
Project the 3D points onto the 2D screen space using a simple projection, such as xs=x and ys=z.

Start with screen coordinates xs and ys.
Use the inverse of the projection to find the corresponding 3D points x and z, setting x=xs and z=ys.
Calculate texture coordinates:
- \theta = \arccos(\frac{z}{r})
- \phi = \arctan(\frac{y}{x})
- S = \frac{\phi}{2\pi}
- T = \frac{\theta}{\pi}

Since a pixel on the screen corresponds to a face on the 3D object, and faces are often triangles, barycentric interpolation is used.
Barycentric interpolation estimates the texture coordinates (S and T) for a point P within a triangle using the texture coordinates of the triangle's vertices.
The coefficients in the interpolation are based on the distances from point P to each vertex. A point closer to a vertex has a higher coefficient.
If the interpolated texture coordinate does not fall exactly on a texel:
- GL_NEAREST: Chooses the nearest texel.
- Linear averaging of neighboring texels can be used to smooth the texture.

Oversampling: if one texel covers multiple pixels.
Undersampling: if one pixel covers multiple texels
In these cases, the texture image must be either super-sampled or down-sampled to match the screen resolution.

Forward Mapping: Common approach, starting from the texture and projecting onto the screen.
Inverse Mapping: Useful when texture is calculated on the fly; it's efficient to calculate only the necessary texture elements.

glGenTextures: Generates texture objects.
glBindTexture: Binds a texture object to a texture type (e.g., GLTEXTURE2D).
glTexImage2D: Sets the texture data.
- Specifies the target (e.g., GLTEXTURE2D), level of detail (for mipmapping), internal format (e.g., GL_RGBA), width, height, border, format, type, and data.

glActiveTexture: Activates a texture unit (e.g., GL_TEXTURE0).
glGetUniformLocation: Retrieves the location of a uniform variable (e.g., texture object) in the shader.
glUniform1i: Sets the value of a uniform variable.
glBindTexture: Binds the texture object to the active texture unit.

Environment mapping simulates reflective surfaces by applying a texture that represents the environment around the object.
Useful when dealing with local illumination models where object-to-object interactions are not computed.
Basic idea: Have a reflective object in the center of a sphere, and take a picture of the reflection of the environemnt on the sphere. Then, map the sphere surface to the reflective object

Instead of a sphere, a cube is used to capture the environment.
A camera is conceptually positioned at the center of the cube, capturing six images (top, bottom, left, right, front, back) corresponding to the cube's faces.
These six images are used as a cube map, which is then applied to the object's surface.
This process must be redone for dynamic scenes where the environment changes.
Frame Buffers: Frame buffers are used to collect the textures from all six faces of the surrounding cube.

Uses a samplerCube uniform instead of sampler2D.
Calculates the reflected vector based on the camera position and the surface normal. The reflect function helps find that vector
Samples the cube map using the reflected vector to determine which part of the environment is reflected at each point on the object.

Textures are used by either using texture2D for texture mapping or cube mapping for textures with six faces
Texture coordinates are the point we sample

Cube map is what changes
SamplerCube is what changes
Reflected direction is what replaces texture coordinates. Can be computed based on where the camera is and the normals at each point.