Mach band effect. The Mach band effect increases the visual unpleasant representation of curved surface using flat shading.

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1 Mach band effect The Mach band effect increases the visual unpleasant representation of curved surface using flat shading. A B : Graphics and Visualization 456

2 Mach band effect The Mach band effect describes the phenomenon that the contrast between adjacent unicolored areas appear higher than actually present due to the human visual apparatus that focuses on extracting contrast : Graphics and Visualization 457

3 Enhanced contrast Shapley : Graphics and Visualization 458

4 Flimmern : Graphics and Visualization 459

5 Also true for colored images : Graphics and Visualization 460

6 What happens when contrast is missing? : Graphics and Visualization 461

7 Back to triangles Standford Teapot : Graphics and Visualization 462

8 Smooth shading Standford Teapot : Graphics and Visualization 463

9 6.2 Gouraud Shading : Graphics and Visualization 464

10 Gouraud shading Gouraud shading computes a smooth continuous shading for surfaces represented by triangular meshes. Each pixel of the projected triangle gets assigned a color individually : Graphics and Visualization 465

11 Outline 1. Apply illumination model at the vertices of the triangular mesh and compute the respective color. 2. Using the colors at the vertices of a triangle, interpolate the color values at the interior points of the triangle. Remark: The interpolation can be executed in screen space, i.e., after the triangle has been projected : Graphics and Visualization 466

12 Smooth shading : Graphics and Visualization 467

13 Normal estimation If the triangular mesh is an approximation of a known analytical function, the function can be evaluated at the respective position : Graphics and Visualization 468

14 Normal estimation for triangular meshes Given all normals of the adjacent triangles, the normal at a vertex of a triangular mesh can be computed as the average of the triangles normals : Graphics and Visualization 469

15 Normal estimation for triangular meshes As the triangles are not of equal size and shape, the average can be weighted accordingly. Example: Weights defined by adjacent angles: : Graphics and Visualization 470

16 Normal estimation by local fitting Normals can also be estimated by locally fitting a surface through the points. Fitting is typically approximate using some kind of minimization such as the least-squares method. One may fit polynomial surfaces of higher degree. It typically suffices to fit a plane and take its normal as an estimate (see Section 2.3) : Graphics and Visualization 471

17 Interpolation Barycentric coordinates: Once the color values are known at the vertices of a triangle, the color values in the interior can be computed using barycentric coordinates : Graphics and Visualization 472

18 Interpolation using scanline algorithm Idea: Exploit knowledge about already computed color values. Traverse projected triangle top-down using scanline. Compute start and end color value of each pixel row using linear interpolation along the triangle s edges. Fill each pixel row using linear interpolation between the start and end color of that row : Graphics and Visualization 473

19 Interpolation using scanline algorithm : Graphics and Visualization 474

20 Gouraud shading : Graphics and Visualization 475

21 Shading in OpenGL Setting State glshademodel( GL_SMOOTH GL_FLAT); GL_FLAT: flat shading GL_SMOOTH: Gouraud shading : Graphics and Visualization 476

22 Gouraud shading: properties Gouraud shading produces smooth transitions of light intensities, but silhouettes remain polygonal. However, typically triangles are small such that this cannot be noticed : Graphics and Visualization 477

23 Gouraud shading: properties Using Gouraud shading, illumination is only evaluated at the vertices of the triangles. Specular highlights that do not stretch over vertices of the mesh are missed. specular highlight : Graphics and Visualization 478

24 Gouraud shading: properties During animation, specular highlights can show some flickering when using Gouraud shading : Graphics and Visualization 479

25 6.3 Phong Shading : Graphics and Visualization 480

26 Phong shading Improve shading by applying the illumination model at each unprojected pixel, i.e., at those points of a triangle that are projected onto a pixel of the screen : Graphics and Visualization 481

27 Phong shading algorithm Use a scanline that traverses the triangle top-down in screen space. For each start and end point of a pixel row, linearly interpolate the surface normal along the triangle s edges. For each pixel row, linearly interpolate the surface normal between start and end point of that row. Apply the illumination model at each unprojected pixel value using the interpolated surface normal : Graphics and Visualization 482

28 Phong shading algorithm Apply same interpolation formula as in Gouraud shading, but interpolate normals instead of color values : Graphics and Visualization 483

29 Phong shading : Graphics and Visualization 484

30 Phong shading: properties Specular highlights are always correctly and exactly computed. Highlights appear much smoother. No flickering during animations : Graphics and Visualization 485

31 Comparison: flat, Gouraud, Phong shading : Graphics and Visualization 486

32 Phong shading: properties The evaluation of the illumination model at each unprojected screen pixel is expensive. Illumination needs to be applied in object space rather than screen space. The pixel can be easily unprojected when storing depth information (cf. depth buffer) : Graphics and Visualization 487

33 Phong shading implementation Phong shading is not supported by OpenGL. It is nowadays implemented using pixel or fragment shaders. The normals can be handed to the shader encoded as colors. Gouraud shading using these colors then interpolates the normals : Graphics and Visualization 488

34 7. Global Illumination : Graphics and Visualization 489

35 Global Illumination The Phong, Blinn-Phong, and BRDF models are local illumination models, i.e., they only take into account the local geometry of an object. Global illumination models take into account the entire geometry that is present in the scene. In particular, global illumination considers the interference of objects with each other. For example, when one object occludes the light source with respect to another object, the other object should appear to be in the shadow of the first object : Graphics and Visualization 490

36 7.1 Ray Tracing : Graphics and Visualization 491

37 Ray tracing Ray tracing is a global illuminiation method. It allows for the computation of all shadows in the scene : Graphics and Visualization 492

38 Observation In nature, light from a light source gets reflected at a point p. The amount of incoming light that is reflected in direction v to the viewer determines the color of the object at position p : Graphics and Visualization 493

39 Ray tracing idea Trace the light ray through the scene. Since many light rays are being sent out from each light source in all directions, this can be computationally very intense. For efficiency purposes, trace in backward direction. Start rays from the viewpoint. Send a ray through each pixel of the screen onto the scene. Trace the ray to the light sources : Graphics and Visualization 494

40 Ray tracing idea light 1 light 2 secondary rays viewpoint object 1 primary ray object 2 screen Primary rays are sent from the viewer through the center of each pixel of the screen When the primary rays hit an object, secondary rays are sent from the point of intersection towards each light source : Graphics and Visualization 495

41 Ray tracing idea light 1 light 2 secondary rays viewpoint object 1 object 2 primary rays screen If a secondary ray hits an object, that object occludes the light source. The color of the pixel is computed by applying a local ilumination model at the position, where the primary ray hits the object, taking into account all light sources that are not occluded : Graphics and Visualization 496

42 Ray-tracing idea : Graphics and Visualization 497

43 Ray-tracing idea : Graphics and Visualization 498

44 Ray-triangle intersection Let the objects be given as triangular meshes. To find intersections of (primary or secondary) rays with the objects, one has to find and compute intersection points of rays with triangles. Ifmanytrianglesarepresentin thescene, onemay want to reduce the amount of triangles that are considered by using spatial partitioning. Spatial partitioning stores for each cell only those triangles that lie (completely or partially) in the cell. The ray-triangle intersection can be limited to those cells that are intersected by the ray (in the order in which it intersects) : Graphics and Visualization 499