Coordinate Systems

1. Coordinate Systems Coordinate Systems (conventional Cartesianreference system) Y Z Y X Z X

2. Transformations Scale Translate • Transformation occurs about the origin of the coordinate system’s axis Rotate

3. Order of Transformations Make a Difference Box centered at origin Rotate about Z 45; Translate along X 1 Translate along X 1; Rotate about Z 45

4. Hierarchy of Coordinate Systems Local coordinate system • Also called: • Scene graphs • Tree structures

5. The Camera Near Clipping Plane Far Clipping Plane Projection Plane View Volume

6. The Camera Parallel Projection Perspective Projection

7. Texture/Realism Perception,Interaction Color Rendering Pipeline Hardware Modelling Transform Visibility Illumination +Shading

8. Polygons, Meshes & Scan Conversion- In scan line rendering (the most common): Each polygon is calculated along each scan line. From the top scan line to the bottom of a frame in the 2D projection plane. V1 Raster Scan line V3 V2

9. Approximating Curved Surfaces with Flat Polygons Flat Shading – each polygon face has a normal that is used to perform lighting calculations.

10. Gouraud Shading • Compute vertex normals by averaging face normals. • Compute intensity at each vertex. I1 Raster Scan line I1,2 I1,2,3,4 I1,3 I3 I2

11. Illumination / Shading • Distinction between illumination and shading models • illumination - calculate intensity at a point on surface • shading - uses calculated intensities to shade polygons (uses illumination models) • we’ll review the important models

12. Illumination / Shading • global illumination: • ray tracing + radiosity • mapping and other techniques • texture maps, bump maps, reflection maps, transparency, anti-aliasing, shadows ray tracing radiosity

13. Local Illumination • Local vs. global illumination models • local (typically) - how is one point of the scene illuminated directly by the light source • is light source only source of illumination? • Simple models lump the rest into a single ambient term • do not account for reflections within the environment

14. Local Illumination • Local vs. global illumination models • global - illuminates the whole scene • typically makes use of local illumination model • incorporates inter-reflectance of objects

15. Lighting Types • Ambient – basic, even illumination of all objects in a scene • Directional – all light rays are in parallel in 1 direction - like the sun • Point – all light rays emanate from a central point in all directions – like a light bulb • Spot – point light with a limited cone and a fall-off in intensity – like a flashlight Cone angle Penumbra angle (light starts to drop offto zero here)

16. Light Effects • Usually only considering reflected part Light reflected specular Light absorbed ambient diffuse transmitted Light=refl.+absorbed+trans. Light=ambient+diffuse+specular

17. Ambient Light • is the light in the environment evenly reaching all surfaces from all directions • light location doesn’t matter • eye position doesn’t matter • IA: ambient light • ka: material’s ambient reflection coefficient

18. Ambient Light • IA: ambient light • ka: material’s ambient reflection coefficient • Models general level of brightness in the scene • Accounts for light effects that are difficult to compute (secondary diffuse reflections, etc)

19. Ambient Light Example

20. Diffuse Light • Light absorbed by the surface and then reflected equally to all directions • Models dullness, roughness of a surface Light Lambert’s Law:(perfectly diffusesurface) N f L • Id: intensity of light source • kd: material’s diffuse reflection coefficient • N: normal vector (normalized) • L: light source vector (normalized)

21. Diffuse Light

22. Diffuse Lighting Example

23. Specular Light • Light that is reflected from the surface unequally to all directions • Models reflections on shiny surfaces Phong’s Law: Light N Eye R f L f a R R R n=small n=large n=inf.

24. Specular light example

25. Specular light calculation • The effect of ‘n’ in the phong model n = 10 n = 90 n = 30 n = 270

26. Shading a Polygon • Illumination Model:determine the color of a surface (data) point by simulating some light attributes. • Local IM:deals only with isolated surface (data) point and direct light sources. • Global IM:takes into account the relationships between all surfaces (points) in the environment. • Shading Model:applies the illumination models at a set of points and colors the whole scene. • Texture Mapping:remappes and avgs. any value above (diffuse) from a 2d picture or map

27. Shading a Polyhedra • Flat (facet) shading: • Works well for objects really made of flat faces. • Appearance depends on number of polygons for curved surface objects. • If polyhedral model is an approximation then need to smooth.

28. Flat and Smooth Shading Getting smooth Curvature : interpolation Flat Shading Gouraud Shading

29. Flat Shading • Polygon meshes approximate smooth curved surfaces with planar facets. Using the previous methods does not generate an illusion of smooth curved surface. N1 N2 • Reason: discontinuity of the normal vectors.

30. Gouraud Shading • Assign vertex the normal of the smooth surface. Or • Average the normal of all neighboring polygons N N1 N2 • Interpolate colors along edges and scan-lines

31. Gouraud shading

32. Phong shading

33. Phong Shading • Gouraud Shading does not properly handle specular highlights. • Reason: Colors are interpolated • Solution: • Compute averaged normal at vertices (Gouraud) • Interpolate normals along edges and scan lines! • Apply illumination model at every pixel

34. Phong Shading Gouraud Shading Phong Shading

35. Specular Large n Small n

36. Textures • Images (textures) applied to polygons (models) to enhance the visual effect of a scene Texture Surface Image Angel Figure 9.3

37. Surface Textures • Add visual detail to surfaces of 3D objects With surface texture Polygonal model

38. Surface Textures • Add visual detail to surfaces of 3D objects

39. Parameterization + = geometry image texture map • Q: How do we decide where on the geometry each color from the image should go?

40. Option: Varieties of projections

41. Texture Mapping • Steps: • Define texture • Specify mapping from texture to surface • Lookup texture values during scan conversion (0,1) y (1,0) t v u x s (0,0) Modeling Coordinate System Texture Coordinate System Image Coordinate System

42. Texture Mapping • When scan convert, map from … • image coordinate system (x,y) to • modeling coordinate system (u,v) to • texture image (t,s) (1,1) (0,1) y (1,0) t v u x s (0,0) Modeling Coordinate System Texture Coordinate System Image Coordinate System

43. Texture Mapping • Interpolate texture coordinates down/across scan lines • U,V mapping can be arbitrary and manipulated • Distortion due to interpolation approximation

44. Texture Filtering • Aliasing is a problem Area filtering Point sampling Angel Figure 9.5

45. Texture Filtering • Size of filter depends on projective warp • Can prefiltering images Magnification Minification Angel Figure 9.14

46. Mip Maps • Keep textures prefiltered at multiple resolutions • For each pixel, linearly interpolate between two closest levels (e.g., trilinear filtering) • Fast, easy for hardware

47. What is a Texture? • MAP surface detail from a predefined (easy table (“texture”) to a simple polygon • Color • Specular ‘color’ (environment map) • Normal vector deviation (bumpmap) • displacement mapping • transparency • ...

48. Bump Mapping • Modifies the direction of the surface normal.

49. Texture andBump Mapping • Diffuse and normal remapping

50. Displacement Mapping • Modifies the surface position in the direction of the surface normal. • the actual geometric position of points over the textured surface are displaced along the surface normal according to the values stored into the texture.