Texture Mapping - Lecture Slides | CSE 167, Study notes of Computer Graphics

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Texture Mapping CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2006 Texture Mapping Texture mapping is the process of mapping an image onto a triangle in order to increase the detail of the rendering This allows us to get fine scale details without resorting to rendering tons of tiny triangles The image that gets mapped onto the triangle is called a texture map or texture and is usually a regular color image Texture Mapping v0 v1 v2 t2 t0 t1 (1,1) (0,0) x y Texture Space Triangle (in any space) Vertex Class We can extend our concept of a Model to include texture coordinates We can do this by simply extending the Vertex class: class Vertex { Vector3 Position; Vector3 Color; Vector3 Normal; Vector2 TexCoord; public: void Draw() { glColor3f(Color.x, Color.y, Color.z); glNormal3f(Normal.x, Normal.y, Normal.z); glTexCoord2f(TexCoord.x, TexCoord.y); glVertex3f(Position.x, Position.y, Position.z); // This has to be last } }; Texture Interpolation The actual texture mapping computations take place at the scan conversion and pixel rendering stages of the graphics pipeline During scan conversion, as we are looping through the pixels of a triangle, we must interpolate the txty texture coordinates in a similar way to how we interpolate the rgb color and z depth values As with all other interpolated values, we must precompute the slopes of each coordinate as they vary across the image pixels in x and y Once we have the interpolated texture coordinate, we look up that pixel in the texture map and use it to color the pixel Pixel Rendering Let’s consider the scan conversion process once again and look at how the pixel rendering process fits in Remember that in scan conversion of a triangle, we loop from the top row down to the bottom row in y, and then loop from left to right in x for each row As we are looping over these pixels, we are incrementing various interpolated values (such as z, r, g, b, tx, and ty) Each of these increments requires only 1 addition per pixel, but perspective correction requires 1 an additional divide per pixel and 1 additional multiply per pixel for each perspective corrected value Before actually writing the pixel, we compare the interpolated z value with the value written into the zbuffer, stored per pixel. If it is further than the existing z value, we don’t render the pixel and proceed to the next one. If it is closer, we finish rendering the pixel by writing the final color into the framebuffer and the new z value into the zbuffer If we are doing expensive per-pixel operations (such as Phong interpolation & per-pixel lighting), we can postpone them until after we are sure that the pixel passes the zbuffer comparison. If we are doing a lot of expensive per- pixel rendering, it is therefore faster if we can render closer objects first Tiling The image exists from (0,0) to (1,1) in texture space, but that doesn’t mean that texture coordinates have to be limited to that range We can define various tiling or wrapping rules to determine what happens when we go outside of the 0…1 range Tiling x y Texture Space (0,0) (1,1) Combinations One can usually set the tiling modes independently in x and y Some systems support independent tiling modes in x+, x-, y+, and y- Texture Space Let’s take a closer look at texture space It’s not quite like the normalized image space or device spaces we’ve seen so far The image itself ranges from 0.0 to 1.0, independent of the actual pixel resolution It allows tiling of values <0 and >1 The individual pixels of the texture are called texels Each texel maps to a uniform sized box in texture space. For example, a 4x4 texture would have pixel centers at 1/8, 3/8, 5/8, and 7/8 Magnification What happens when we get too close to the textured surface, so that we can see the individual texels up close? This is called magnification We can define various magnification behaviors such as: Point sampling Bilinear sampling Bicubic sampling Minification Why is it necessary to have special handling for minification? What happens if we just take our per-pixel texture coordinate and use it to look up the texture at a single texel? Just like magnification, we can use a simple point sampling rule for minification However, this can lead to a common texture problem known as shimmering or buzzing which is a form of aliasing Consider a detailed texture map with lots of different colors that is only being sampled at a single point per pixel If some region of this maps to single pixel, the sample point could end up anywhere in that region. If the region has large color variations, this may cause the pixel to change color significantly even if the triangle only moves a minute amount. The result of this is a flickering/shimmering/buzzing effect To fix this problem, we must use some sort of minification technique Minification Ideally, we would look at all of the texels that fall within a single pixel and blend them somehow to get our final color This would be expensive, mainly due to memory access cost, and would get worse the farther we are from the texture A variety of minification techniques have been proposed over the years (and new ones still show up) One of the most popular methods is known as mipmapping Mipmapping Mipmapping was first published in 1983, although the technique had been in use for a couple years at the time It is a reasonable compromise in terms of performance and quality, and is the method of choice for most graphics hardware In addition to storing the texture image itself, several mipmaps are precomputed and stored Each mipmap is a scaled down version of the original image, computed with a medium to high quality scaling algorithm Usually, each mipmap is half the resolution of the previous image in both x and y For example, if we have a 512x512 texture, we would store up to 8 mipmaps from 256x256, 128x128, 64x64, down to 1x1 Altogether, this adds 1/3 extra memory per texture (1/4 + 1/16 + 1/64…= 1/3) Usually, texture have resolutions in powers of 2. If they don’t, the first mipmap (the highest res) is usually the original resolution rounded down to the nearest power of 2 instead of being half the original res. This causes a slight memory penalty Non-square textures are no problem, especially if they have power of 2 resolutions in both x and y. For example, an 16x4 texture would have mipmaps of 8x2, 4x1, 2x1, and 1x1 Anisotropic Mipmapping Modern graphics hardware supports a feature called anisotropic mipmapping which attempts to address the edge-on blurring issue With this technique, rectangular mipmaps are also stored in addition to the square ones. Usually aspect ratios of 2x1 or 4x1 are chosen as limits In other words, a 512x512 texture with 2x1 anisotropic mipmapping would store mipmaps for: 256x512, 512x256, 256x256, 256x128, 128x256, 128x128… 2x1, 1x2, 1x1 Regular mipmapping (1x1 aspect) adds 1/3 memory per texture 2x1 aspect adds 2/3 extra memory per texture 4x1 aspect adds 5/6 extra memory per texture Anisotropic mipmapping improves image quality for edge on situations, but the high aspect rectangles are still xy aligned, and so the technique doesn’t work well for diagonal viewing situations In fact, 4x1 aspect and higher can tend to have noticeably varying blur depending on the view angle. This would be noticed if one was standing on a large relatively flat surface (like the ground) and turning around in place Anisotropic mipmapping adds little hardware complexity and runtime cost, and so is supported by modern graphics hardware. It is an improvement over the standard technique, but is still not ideal Eliptical Weighted Averaging Present day realtime graphics hardware tends to use mipmapping or anisotropic mipmapping to fix the texture buzzing problem Some high quality software renderers use these methods as well, or enhanced variations Perhaps the highest quality technique (though not the fastest!) is one called eliptical weighted averaging or EWA This technique is based on the fact that a circle in pixel space maps to an ellipse in texture space We want to sample all of the texture that falls within the pixel, however, we will weight the texels higher based on how close they are to the center of the pixel We use some sort of radial distribution to define how the pixel is sampled. A common choice is a radial Gaussian distribution Each concentric circle in this distribution maps to a ellipse in texture space, so the entire radial Gaussian distribution of a pixel maps to a series of concentric ellipses in texture space With the EWA technique, we sample all of the texels, weighted by their location in this region This technique represents the theoretically best way to sample the texture, but is really only useful in theory, as it can be prohibitively expensive in real situations There are some advanced mipmapped EWA techniques where the EWA actually performs a relatively small number of samples from mipmapped textures. This method combines the best of both techniques, and offers a fast, high quality, hardware friendly technique for texture sampling. However, it is fairly new and not used in any production hardware that I know of. Antialiasing These minification techniques (mipmapping, EWA) address the buzzing/shimmering problems we see when we view textures from a distance These techniques fall into the broader category of antialiasing techniques, as texture buzzing is a form of aliasing We will discuss more about aliasing and antialiasing in a later lecture Orthographic Mapping Orthographic mappings are very common and simple We might use this in the offline modeling process to map a brick texture onto the side of a building, or a grass texture onto a terrain We can also use it dynamically in a trick for computing shadows from a directional light source Perspective Mapping Perspective mappings tend to be useful in situations where one uses a texture map to achieve lighting effects For example, one can achieve a slide projector effect by doing a perspective projection of a texture map on to an object It is also useful in certain shadow tricks, like the orthographic mapping Spherical Mapping A variety of spherical mappings can be constructed, but the most common is a polar mapping Think of the texture image itself getting mapped onto a giant sphere around our object, much like a map of the earth The tx coordinate maps to the longitude and the ty coordinate maps to latitude Then think of this sphere being shrink wrapped down to project onto the object This technique is useful for mapping relatively round object, such as a character’s head and face Environment Mapping Environment mapping is a simple but powerful technique for faking mirror-like reflections It is also known as reflection mapping It is performed dynamically each frame for each vertex, and is based on the camera’s position Environment mapping is similar to the spherical mapping, in that we start by visualizing a giant sphere centered at the camera, with the texture mapped onto it in a polar fashion For each vertex, we compute the vector e from the vertex to the eye point. We then compute the reflection vector r, which is e reflected by the normal We assume that r hits our virtual spherical surface at somewhere, so we use that as the texture coordinate Environment Mapping e n r ( ) ( ) ( ) π π π π 2asin 2 ,2atan 2 + = + = −⋅= y y xz x r t rrt enner Cube Mapping Cube mapping is essentially an enhancement to sphere mapping and environment mapping As both of those techniques require polar mappings, both of them suffer from issues near the actual poles, where the entire upper and lower rows of the image get squashed into a single point Cube or box mapping uses six individual square texture maps mapped onto a virtual cube, instead of a single texture mapped onto a virtual sphere The result is that one gets a cleaner mapping without visual problems It can also save memory, as the total number of texels can often be smaller for equal or better visual quality It also should run faster, as it only requires some comparison logic and a single division to get the final texture coordainte, instead of inverse trigonometric functions It also has the advantage in that the six views are simple 90 degree perspective projections and can actually be rendered on the fly! Bump Mapping As we said, a texture doesn’t always have to represent a color image The technique of bump mapping uses a texture to represent the variable height of a surface For example, each texel could store a single 8 bit value which represents some variation from a mean height Bump mapping is used in conjunction with Phong shading (interpolating normals across the triangle and applying the lighting equations per pixel) The Phong shading provides an interpolated normal per pixel, which is then further perturbed according to the bump map This perturbed normal is then used for per-pixel lighting This allows one to use a bump map to fake small surface irregularities that properly interact with lighting Bump mapping is definitely a hack, as a triangle still looks flat when viewed edge-on. However, it is a very popular technique and can be very useful for adding subtle shading details State of the art graphics hardware supports Phong shading, bump mapping, and per pixel lighting Displacement Mapping The more advanced technique of displacement mapping starts with the same idea as bump mapping Instead of simply tweaking the normals, the displacement mapping technique perturbs the actual surface itself This essentially requires dicing the triangle up into lots of tiny triangles (often about 1 pixel in size) Obviously, this technique is very expensive, but is often used in high quality rendering