# Interpolation using scanline algorithm

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1 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 454

2 Interpolation using scanline algorithm : Graphics and Visualization 455

3 Gouraud shading : Graphics and Visualization 456

5 Gouraud shading 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 458

6 Gouraud shading 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 459

7 Gouraud shading During animation, specular highlights can show some flickering when using Gouraud shading : Graphics and Visualization 460

8 6.3 Phong Shading : Graphics and Visualization 461

9 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 462

10 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 463

11 Phong shading algorithm Apply same interpolation formula as in Gouraud shading, but interpolate normals instead of color values : Graphics and Visualization 464

12 Phong shading : Graphics and Visualization 465

13 Phong shading Specular highlights are always correctly and exactly computed. Highlights appear much smoother. No flickering during animations : Graphics and Visualization 466

14 Comparison: flat, Gouraud, Phong shading : Graphics and Visualization 467

15 Phong shading 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 468

16 Phong shading 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 469

17 7. Global Illumination : Graphics and Visualization 470

18 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 471

19 7.1 Ray Tracing : Graphics and Visualization 472

20 Ray tracing Ray tracing is a global illuminiation method. It allows for the computation of all shadows in the scene : Graphics and Visualization 473

21 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 474

22 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 475

23 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 476

24 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 477

25 Ray-tracing idea : Graphics and Visualization 478

26 Ray-tracing idea : Graphics and Visualization 479

27 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 480

28 Ray-triangle intersection 1. Compute intersection of ray with plane. 2. Check whether intersection point lies within the triangle : Graphics and Visualization 481

29 Ray-triangle intersection Compute intersection of ray with plane : Graphics and Visualization 482

30 Ray-triangle intersection : Graphics and Visualization 483

31 Ray-triangle intersection : Graphics and Visualization 484

32 convex polygons Other polygons plane-intersection: like triangles inside test: algebraically concave polygons plane-intersection: like triangles inside test: ray intersection non-planar polygons triangulate : Graphics and Visualization 485

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