大三05计算机图形学-88texture mapping

1、Texture Mapping纹理映射原著Ed AngelProfessor of Computer Science, Electrical and Computer Engineering, and Media ArtsUniversity of New Mexico编辑 武汉大学计算机学院图形学课程组ObjectivesIntroduce Mapping Methods介绍各种映射方法Texture Mapping纹理映射Environment Mapping环境映射Bump Mapping凹凸映射Consider basic strategies考虑基本策略Forward vs back

2、ward mapping正向映射和逆向映射Point sampling vs area averaging点采样与区域平均The Limits of Geometric Modeling几何建模的局限Although graphics cards can render over 10 million polygons per second, that number is insufficient for many phenomena虽然图形显示卡可以每秒钟显示多达一千万个多边形，但这个速度仍不能满足模拟许多自然现象和天然物质的要求Clouds云Grass草Terrain地貌Skin毛发树皮水波

3、与火焰Modeling an Orange橙子的模型Consider the problem of modeling an orange (the fruit)考虑如何建立橙子的模型Start with an orange-colored sphere用橙色的球表示橙子Too simple太简单Replace sphere with a more complex shape用更复杂形状代替球Does not capture surface characteristics (small dimples)没有表示出表面的特性(微凹, dimples)Takes too many polygons

4、to model all the dimples为了模拟所有的微凹，需要相当多的多边Modeling an Orange橙子的模型(2)Take a picture of a real orange, scan it, and “paste” onto simple geometric model获取真实橙子的照片，扫描后把结果“粘贴”到简单的几何模型上This process is known as texture mapping这个过程就是纹理映射Still might not be sufficient because resulting surface will be smooth可能

5、结果仍然不令人满意，因为所得曲面是光滑的Need to change local shape需要改变局部形状Bump mapping凹凸映射Three Types of Mapping三种映射方法Texture Mapping纹理映射Uses images to fill inside of polygons利用图像填充多边形Environment (reflection) mapping环境映射(反射映射)Uses a picture of the environment for texture maps利用环境的图像进行纹理映射Allows simulation of highly spe

6、cular surfaces可以模拟高度镜面曲面Bump mapping凹凸映射Emulates altering normal vectors during the rendering process在生成显示结果的过程中可以改变法向量Texture Mapping纹理映射geometric model几何模型texture mapped纹理映射后Environment Mapping环境映射Bump Mapping凹凸映射三种映射的共同点作为片元处理的一部分，改变单个片元的明暗值都与存储为一维、二维或三维数字图像的贴图有关保持低的几何复杂性，但能产生复杂几何的视觉效果都可能产生走样误差Wh

7、ere does mapping take place?映射在什么地方进行？Mapping techniques are implemented at the end of the rendering pipeline映射技术是在绘制流水线的最后阶段实现的Very efficient because few polygons make it past the clipper非常有效，因为在经过所有的操作后，减少了许多不必要的映射二维纹理纹理：以数组形式存储在处理器内存里的二维图像，此时数组元素称为纹素(texel)由成 应用程序生成 或 照片扫描输入把离散数组看成一个连续的二维矩形区域纹理图案

8、T(s,t)，独立变量s和t是纹理坐标一般把纹理坐标缩放到0,1区间Is it simple?很容易吗？Although the idea is simple-map an image to a surface-there are 3 or 4 coordinate systems involved虽然映射的想法很简单，即把图像映射到曲面上，但由于这时要用到三、四个坐标系，因此实现起来并不容易2D image3D surfaceCoordinate Systems坐标系Parametric coordinates参数坐标系May be used to model curves and surf

9、aces可以用来建立曲线、曲面 Texture coordinates纹理坐标系Used to identify points in the image to be mapped用来识别要被映射的图像上的点 Object or World Coordinates世界坐标系Conceptually, where the mapping takes place从概念上说，就是映射发生的地方 Window Coordinates屏幕坐标系Where the final image is really produced最终图像生成的地方Texture Mapping纹理映射框架parametric c

10、oordinatestexture coordinatesworld coordinateswindow coordinatesMapping Functions映射函数Basic problem is how to find the maps基本问题就是如何定义映射Consider mapping from texture coordinates to a point a surface考虑从纹理坐标到曲面上一点的映射Appear to need three functions直观地看，应当需要三个函数x = x(s,t)y = y(s,t)z = z(s,t)But we really w

11、ant to go the other way虽然从概念上讲，最终必定用到上述的函数，但实际采用的是却是间接的方法ts(x,y,z)Backward Mapping逆映射We really want to go backwards我们需要的是逆向操作Given a pixel, we want to know to which point on an object it corresponds给定一个像素，我们想知道它对应于对象上的哪个点Given a point on an object, we want to know to which point in the texture it co

12、rresponds给定对象上的一个点，我们想知道它对应于纹理中的哪个点Need a map of the form此时需要如下形式的映射s = s(x,y,z)t = t(x,y,z)Such functions are difficult to find in general这样的函数一般是很难求出来的Two-part mapping两步映射 One solution to the mapping problem is to first map the texture to a simple intermediate surface解决映射问题的另外一种方法,首先把纹理映射到一个简单的中间曲

13、面上Example: map to cylinder例如：映射到圆柱上Cylindrical Mapping圆柱面映射parametric cylinder高为h，半径为r圆柱的参数方程是x = r cos 2p uy = r sin 2puz = v/hmaps rectangle in u,v space to cylinder of radius r and height h in world coordinates映射函数s = ut = vmaps from texture space从纹理坐标到圆柱面上没有变形适合于构造与无底的圆柱面拓朴同构的曲面上的纹理Spherical Map

14、球面映射We can use a parametric sphere半径为r的球的参数方程x = r cos 2puy = r sin 2pu cos 2pvz = r sin 2pu sin 2pvhave to decide where to put the distortion类似于地图绘制中的映射，存在变形Spheres are used in environmental maps用在环境映射中Box Mapping立方体映射Easy to use with simple orthographic projection适合应用于正交投影Also used in environment

15、maps也用在环境映射中Second Mapping两步映射中的第二个映射Map from intermediate object to actual object从中间对象到实际对象的映射Normals from intermediate to actual从中间形状的法向到实际对象Normals from actual to intermediate从实际对象的法向到中间形状Vectors from center of intermediate从实际对象的中心开始的向量31其它类型的纹理立体纹理程序生成的纹理Procedural textureAliasing走样Point sampling of the texture can lead to aliasing error