Introduction and Basic OpenGL functionality Texture Mapping Introduction and Basic OpenGL functionality

Why Texture Map? How can we model this scene with polygons? Lots of detail means lots of polygons to render 100’s, 1000’s, Millions of polygons! Can be difficult to model fine features

Review: Why Texture Map? (2) What if we render just one polygon with a picture of a brick wall mapped to it? The graphics hardware is faster at texture mapping than processing many polygons

Textures Provide Realism Spatially-varying modification of surface appearance at the pixel level Characteristics Color Shininess Transparency Bumpiness Etc.

Our Goal

Texture Mapping Overview texture coordinates Object Space World Space Model Transform Projection/ Clipping Texture Space Screen Space Viewport Transform Window Space Rasterization Texture mapping

Texture mapping: Steps Creation: Where does the texture image come from, i.e. sources? Parameterization: Mapping from 3-D shape locations (x, y, z) to 2-D texture image coordinates (s, t) Rasterization (Sampling and Interpolation): What do we draw at each pixel?

Texturing: Creation Reproductions Directly-computed functions Photographs Handpainted Download from the web Directly-computed functions e.g., lightmaps Procedurally-built Synthesize with randomness, pattern-generating rules, etc. Remember our checkerboard procedure? courtesy of H. Elias

Enable (Disable) Textures Enable texture – glEnable(GL_TEXTURE_2D) Disable texture – glDisable(GL_TEXTURE_2D) Remember to disable texture mapping when you draw non-textured polygons

Texturing: Parameterization (Simple) Assign texture coordinates to the polygon vertices (in object space) We did this in Lab1. Simple Case Apply a 2D texture onto a quadrilateral (0,0) (1,0) (1,1) (0,1) s t (0,0) (1,1)

Texturing: Parameterization (Object Mesh) How do we assign texture coordinates to objects? Problem: Map from 3D to 2D Idea: Map (x, y, z) to an intermediate space (u, v) Projector function to obtain object surface coordinates (u, v) Corresponder function to find texel coordinates (s, t) Filter texel at (s, t) Modify pixel (i, j) Rasterization courtesy of R. Wolfe list adapted from Akenine-Moller & Haines

Projector Functions How do we map the texture onto a arbitrary (complex) object? Construct a mapping between the 3-D point to an intermediate surface Why? The intermediate surface is simple  we know its characteristics Still a 3D surface, but easier to map to texture space (2D) Easy to parameterize the intermediate surface in 2D, i.e. (u, v) space Idea: Project each object point to the intermediate surface with a parallel or perspective projection The focal point is usually placed inside the object Plane Cylinder Sphere Cube Mesh: piece-wise planar courtesy of R. Wolfe Planar projector

Planar Projector u = x, v = y Orthographic projection onto XY plane: courtesy of R. Wolfe ...onto YZ plane ...onto XZ plane

Cylindrical Projector Convert rectangular coordinates (x, y, z) to cylindrical (r, µ, h), use only (h, µ) to index texture image courtesy of R. Wolfe

Spherical Projector Convert rectangular coordinates (x, y, z) to spherical (, φ) courtesy of R. Wolfe

Surface Patches A polygon or mesh of polygons defining a surface Map four corners of a quad to (u, v) values courtesy of R. Wolfe

Parametric Surfaces A parameterized surface patch x = f(u, v), y = g(u, v), z = h(u, v) You will get to these kinds of surfaces in CSE 784. courtesy of R. Wolfe

Examples: Courtesy of Jason Bryan planar spherical cylindrical surface patch

Notice Distortions Due To Object Shape Watt planar cylindrical spherical

Specify texture coordinates Give texture coordinates before defining each vertex glBegin(GL_QUADS); glTexCoord2D(0,0); glVertex3f(-0.5, 0, 0.5); … glEnd();

Transform texture coordinates All the texture coordinates are multiplied by Gl_TEXTURE matrix before in use To transform texture coordinates, you do: glMatrixMode(Gl_TEXTURE); Apply regular transformation functions Then you can draw the textured objects

Texture Representation Bitmap (pixel map) textures (supported by OpenGL) Procedural textures (used in advanced rendering programs) Bitmap texture: A 2D image - represented by 2D array texture[height][width] Each pixel (or called texel ) by a unique pair texture coordinate (s, t) The s and t are usually normalized to a [0,1] range For any given (s,t) in the normalized range, there is a unique image value (i.e., a unique [red, green, blue] set ) s t (0,0) (1,1)

Map textures to surfaces Establish mapping from texture to surfaces (polygons): - Application program needs to specify texture coordinates for each corner of the polygon (0,0) (1,0) (1,1) The polygon can be in an arbitrary size

Map textures to surfaces Texture mapping is performed in rasterization (backward mapping) (1,1) (0,1) For each pixel that is to be painted, its texture coordinates (s, t) are determined (interpolated) based on the corners’ texture coordinates (why not just interpolate the color?) The interpolated texture coordinates are then used to perform texture lookup (0,0) (1,0)

Texture Mapping 1. projection 3. patch texel 3D geometry 2. texture lookup 2D projection of 3D geometry S t 2D image

Inverse Mapping Screen space → … → object space → texture space World Space Clip Space S t Screen Space Object Space Texture Space

Texture Value Lookup For the given texture coordinates (s,t), we can find a unique image value from the texture map (1,1) How about coordinates that are not exactly at the intersection (pixel) positions? Nearest neighbor Linear Interpolation Other filters (0,0) (0.25,0) (0.5,0) (0.75,0) (1,0)

OpenGL texture mapping Steps in your program 1) Specify texture read or generate image Assign to texture 2) Specify texture mapping parameters Wrapping, filtering, etc. 3) Enable GL texture mapping (GL_TEXTURE_2D) 4) Assign texture coordinates to vertices 5) Draw your objects 6) Disable GL texture mapping (if you don’t need to perform texture mapping any more)

Specify textures Load the texture map from main memory to texture memory glTexImage2D(Glenum target, Glint level, Glint iformat, int width, int height, int border, Glenum format, Glenum type, Glvoid* img) Example: glTeximage2D(GL_TEXTURE_2D, 0, GL_RGB, 64, 64, 0, GL_RGB, GL_UNSIGNED_BYTE, myImage); (myImage is a 2D array: GLuByte myImage[64][64][3]; ) The dimensions of texture images must be powers of 2

Fix texture size If the dimensions of the texture map are not power of 2, you can Pad zeros 2) use gluScaleImage() 60 Ask OpenGL to filter the data for you to the right size – you can specify the output resolution that you want 100 128 Remember to adjust the texture coordinates for your polygon corners – you don’t want to Include black texels in your final picture 64

An Interactive Introduction to OpenGL Programming Texture Objects Like display lists for texture images one image per texture object may be shared by several graphics contexts Generate texture names glGenTextures( n, *texIds ); The first step in creating texture objects is to have OpenGL reserve some indices for your objects. glGenTextures() will request n texture ids and return those values back to you in texIds. To begin defining a texture object, you call glBindTexture() with the id of the object you want to create. The target is one of GL_TEXTURE_{123}D(). All texturing calls become part of the object until the next glBindTexture() is called. To have OpenGL use a particular texture object, call glBindTexture() with the target and id of the object you want to be active. To delete texture objects, use glDeleteTextures( n, *texIds ), where texIds is an array of texture object identifiers to be deleted.

Texture Objects (cont.) An Interactive Introduction to OpenGL Programming Texture Objects (cont.) Create texture objects with texture data and state glBindTexture( target, id ); Bind textures before using

An Interactive Introduction to OpenGL Programming Specify Texture Image CPU DL Poly. Per Vertex Raster Frag FB Pixel Texture Define a texture image from an array of texels in CPU memory glTexImage2D( target, level, components, w, h, border, format, type, *texels ); dimensions of image must be powers of 2 Texel colors are processed by pixel pipeline pixel scales, biases and lookups can be done Specifying the texels for a texture is done using the glTexImage{123}D() call. This will transfer the texels in CPU memory to OpenGL, where they will be processed and converted into an internal format. The array of texels sent to OpenGL with glTexImage*() must be a power of two in both directions. An optional one texel wide border may be added around the image. This is useful for certain wrapping modes. The level parameter is used for defining how OpenGL should use this image when mapping texels to pixels. Generally, you’ll set the level to 0, unless you’re using a texturing technique called mipmapping, which we’ll discuss in a few slides.

Converting A Texture Image An Interactive Introduction to OpenGL Programming Converting A Texture Image If dimensions of image are not power of 2 gluScaleImage( format, w_in, h_in, type_in, *data_in, w_out, h_out, type_out, *data_out ); *_in is for source image *_out is for destination image Image interpolated and filtered during scaling If your image does not meet the power of two requirement for a dimension, the gluScaleImage() call will resample an image to a particular size. It uses a simple box filter to interpolate the new images pixels from the source image. Additionally, gluScaleImage() can be used to convert from one data type ( i.e. GL_FLOAT ) to another type, which may better match the internal format in which OpenGL stores your texture. Note that use of gluScaleImage() can also save memory.

Wrapping Modes repeat: Start entire texture over (0, 0) (3, 0) (3, 3) (0, 3) repeat: Start entire texture over mirror: Flip copy of texture in each direction Get continuity of pattern Rather new OpenGL feature. clamp to edge: Extend texture edge pixels clamp to border: Surround with border color courtesy of Microsoft

Texture mapping parameters Example: glTexParameteri(GL_TEXTAURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP) GL_Repeat (0,0) (2,2) (0,0) (2,2) GL_Clamp If (s >1) s = 1 If (t >1) t = 1 (0,0) (1,1) texture

Texture mapping parameters(2) Since a polygon can get transformed to arbitrary screen size, texels in the texture map can get magnified or minified. Filtering: interpolate a texel value from its neighbors or combine multiple texel values into a single one texture texture polygon projection polygon projection Magnification Minification

Texture mapping parameters(3) OpenGL texture filtering: 2) Linear interpolate the neighbors (better quality, slower) glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR) Nearest Neighbor (lower image quality) glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); Or GL_TEXTURE_MAX_FILTER

Texture color blending Determine how to combine the texel color and the object color GL_MODULATE – multiply texture and object color GL_BLEND – linear combination of texture and object color GL_REPLACE – use texture color to replace object color Example: glTexEnvf(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE);

Texture Application Modes decal: Overwrite object’s color or material with texel modulate: Combine object pixel with texel via multiplication courtesy of Microsoft

Put it all together … glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); glTexEnvf(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE); glEnable(GL_TEXTURE_2D); glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, 64, 64, 0, GL_RGB, GL_UNSIGNED_BYTE, mytexture); Draw_picture1(); // define texture coordinates and vertices in the function ….

Advanced: Multitexture + Modulation New cards can modulate multiple textures CSE 781 will examine many uses of texture mapping. courtesy of K. Miller X = Light Map

Multi-texturing: Multiplication *

Multi-texturing: Addition + =

[Images courtesy of www.gamasutra.com] Light maps Also can avoid the expensive lighting calculations. Right: Light Map applied Left: No Light Map applied [Images courtesy of www.gamasutra.com]

Light Maps: Quake

Simple Applications: Billboards from Akenine-Moller & Haines

Texture Rasterization Texture coordinates are interpolated from polygon vertices just like … remember … Color : Gouraud shading Depth: Z-buffer First along polygon edges between vertices Then along scanlines between left and right sides from Hill

Linear Texture Coordinate Interpolation This doesn’t work in perspective projection! The textures look warped along the diagonal Noticeable during an animation courtesy of H. Pfister

Why? Equal spacing in screen (pixel) space is not the same as in texture space in perspective projection Perspective foreshortening from Hill courtesy of H. Pfister

Perspective-Correct Texture Coordinate Interpolation Interpolate (tex_coord/w) over the polygon, then do perspective divide after interpolation Compute at each vertex after perspective transformation “Numerators” s/w, t/w “Denominator” 1/w Linearly interpolate 1/w, s/w, and t/w across the polygon At each pixel Perform perspective division of interpolated texture coordinates (s/w, t/w) by interpolated 1/w (i.e., numerator over denominator) to get (s, t)

Perspective-Correct Interpolation That fixed it!

Perspective-Correct Interpolation: Notes But we didn’t do this for Gouraud shading… Actually, we should have, but the error is not as obvious Alternative: Use regular linear interpolation with small enough polygons that effect is not noticeable Linear interpolation for Z-buffering is correct

Perspective Correction Hint Texture coordinate and color interpolation: Linearly in screen space (wrong) OR Persective correct interpolation (slower) glHint (GL_PERSPECTIVE_CORRECTION_HINT, hint), where hint is one of: GL_NICEST: Perspective GL_FASTEST: Linear GL_DONT_CARE: Linear

An Interactive Introduction to OpenGL Programming Texture Objects Like display lists for texture images one image per texture object may be shared by several graphics contexts Generate texture names glGenTextures( n, *texIds ); The first step in creating texture objects is to have OpenGL reserve some indices for your objects. glGenTextures() will request n texture ids and return those values back to you in texIds. To begin defining a texture object, you call glBindTexture() with the id of the object you want to create. The target is one of GL_TEXTURE_{123}D(). All texturing calls become part of the object until the next glBindTexture() is called. To have OpenGL use a particular texture object, call glBindTexture() with the target and id of the object you want to be active. To delete texture objects, use glDeleteTextures( n, *texIds ), where texIds is an array of texture object identifiers to be deleted.

Texture Objects (cont.) An Interactive Introduction to OpenGL Programming Texture Objects (cont.) Create texture objects with texture data and state glBindTexture( target, id ); Bind textures before using

Texture Animation Just change the texture coordinates

Texture Animation Sprite Animations

Sprites and Billboards Sprites – usually refer to 2D animated characters that move across the screen. Like Pacman Three types (or styles) of billboards Screen-aligned (parallel to top of screen) World aligned (allows for head-tilt) Axial-aligned (not parallel to the screen)

Creating Billboards in OpenGL Annotated polygons do not exist with OpenGL 1.3 directly. If you specify the billboards for one viewing direction, they will not work when rotated.

Example

Example 2 The alpha test is required to remove the background. More on this example when we look at depth textures.

Re-orienting Billboards need to be re-oriented as the camera moves. This requires immediate mode (or a vertex shader program). Can either: Recalculate all of the geometry. Change the transformation matrices.

Re-calculating the Geometry Need a projected point (say the lower-left), the projected up-direction, and the projected scale of the billboard. Difficulties arise if we are looking directly at the ground plane.

Undo the Camera Rotations Extract the projection and model view matrices. Determine the pure rotation component of the combined matrix. Take the inverse. Multiply it by the current model-view matrix to undo the rotations.

Screen-aligned Billboards Alternatively, we can think of this as two rotations. First rotate around the up-vector to get the normal of the billboard to point towards the eye. Then rotate about a vector perpendicular to the new normal orientation and the new up-vector to align the top of the sprite with the edge of the screen. This gives a more spherical orientation. Useful for placing text on the screen.

World Aligned Billboards Allow for a final rotation about the eye-space z-axis to orient the billboard towards some world direction. Allows for a head tilt.

Example Lastra

Example Lastra

Axial-Aligned Billboards The up-vector is constrained in world-space. Rotation about the up vector to point normal towards the eye as much as possible. Assuming a ground plane, and always perpendicular to that. Typically used for trees.

Fin Billboard Use two polygons at right angles. Typically right angles.

OpenGL Architecture CPU Display List Polynomial Evaluator Per Vertex Operations & Primitive Assembly Rasterization Per Fragment Operations Frame Buffer Texture Memory CPU Pixel

Per-Fragment Operations Per Vertex Operations & Primitive Assembly Polynomial Evaluator Display List Per Fragment Operations Frame Buffer CPU Rasterization Texture Memory Pixel Operations

Getting to the Framebuffer Blending Depth Test Dithering Logical Operations Scissor Stencil Alpha Fragment Framebuffer In order for a fragment to make it to the frame buffer, it has a number of testing stages and pixel combination modes to go through. The tests that a fragment must pass are: scissor test - an additional clipping test alpha test - a filtering test based on the alpha color component stencil test - a pixel mask test depth test - fragment occlusion test Each of these tests is controlled by a glEnable() capability. If a fragment passes all enabled tests, it is then blended, dithered and/or logically combined with pixels in the framebuffer. Each of these operations can be enabled and disabled.

Alpha Test Reject pixels based on their alpha value glAlphaFunc( func, value ) glEnable( GL_ALPHA_TEST ) Use alpha as a mask in textures Alpha values can also be used for fragment testing. glAlphaFunc() sets a value which, if glEnable(GL_ALPHA_TEST) has been called, will test every fragment’s alpha against the value set, and if the test fails, the fragment is discarded. The functions which glAlphaFunc() can use are: GL_NEVER GL_LESS GL_EQUAL GL_LEQUAL GL_GREATER GL_NOTEQUAL GL_GEUQAL GL_ALWAYS The default is GL_ALWAYS, which always passes fragments. Alpha testing is particularly useful when combined with texture mapping with textures which have an alpha component. This allows your texture map to act as a localized pixel mask. This technique is commonly used for objects like trees or fences, where modeling the objects (and all of its holes) becomes prohibitive.

Billboard Clouds Add several planes for different parts of the model (images from Univ. of Utah).

Demo - SpeedTree

Shaders allow better animation Teaser for CSE 781 Pretty water: http://www.cogfilms.com/index-2006.html