1. Radiosity, Surface Detail, Textures
EEL
Introduction to Computer Graphics
Radiosity, Surface Detail, Textures
Saravanan Manoharan

2. Overview: Radiosity - Intensity - Radiant flux
- Form factor & Equation
- Radiosity equation
- Progressive refinement
Surface detail
- Texture
- Bump mapping
- Frame mapping
- wire frame
Non- photorealistic rendering
- Hatching & cross hatching
- pen and ink techniques
- Artistic style rendering
- Mosaic rendering

3. RADIOSITY:
A rendering method that simulates light reflecting off one surface and onto another. It is a more accurate method of rendering light and shadows than ray tracing
Radiosity produces the soft shadows from multiple reflect-ions and light sources that exist in the real world
Global illumination algorithm: illumination arriving on a surface comes not just directly from the light sources, but also from other surfaces reflecting light

4. Scene without radiosity
Same scene with radiosity

5. Radiosity is the energy leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy
Bi is the radiosity of patch i. Ei is emitted energy. Ri is the reflectivity of the patch, giving reflected energy by multiplying by the incident energy (the energy which arrives from other patches). All j () in the rendered environment are integrated for BjFjidAj, to determine the energy leaving each patch j that arrives at patch i. Fji is a constant form factor for the geometric relation between patch i and each patch j.

6. Intensity Intensity: RGB components weighted equally
Eye is sensitive to ratios of intensity rather than absolute intensity levels
Most displays output light intensity: L = kNγ where N is number of electrons in the beam and γ is usually
Intensity attenuates in proportion to distance from source
SOLID ANGLE:
A solid angle is a 3D angular volume that is defined analogously to the definition of a plane angle in two dimensions.

7. Intensity, I, is the flux per unit solid angle
Intensity, I, is the flux per unit solid angle. It is the amount of flux from a point source contained in a small angular volume.
Steradian (sr): The solid angle subtended at the center of a sphere by an area on its surface numerically equal to the square of the radius
When the solid angle is large enough so that the angle with the surface normal is not the same over the entire solid angle, the total projected solid angle must be computed by integrating the incremental projected solid angles

8. Radiant Flux:
Light “flows” through space, and so radiant power is more commonly referred to as the “time rate of flow of radiant energy,” or radiant flux.
Φ = dQ/dt
where Q is radiant energy and t is time. In terms of a photographic light meter measuring visible light, the instantaneous magnitude of the electric current is directly proportional to the radiant flux.

9. Form Factor:
In radiosity, the surfaces of the scene to be rendered are each divided up into one or more smaller surfaces (patches). A form factor is computed for each pair of patches; it is a coefficient describing how well the patches can see each other. Patches that are far away from each other, or oriented at oblique angles relative to one another, will have smaller view factors.
The form factor in the above equation is defined to be the fraction of energy that leaves surface i and lands on surface j

10. Radiosity equation:
Radiosity B is the energy per unit area leaving the patch surface per discrete time interval and is the combination of emitted and reflected energy:
B(x)i dAi - total energy leaving a small area dAi around a point x.
E(x)i dAi is the emitted energy.
ρ(x) is the reflectivity of the point, giving reflected energy per unit area by multiplying by the incident energy per unit area (the total energy which arrives from other patches).
S denotes that the integration variable x' runs over all the surfaces in the scene
r is the distance between x and x‘
If the surfaces are approximated by a finite number of planar patches, each of which is taken to have a constant radiosity Bi and reflectivity ρi, the above equation gives the discrete radiosity equation,

11. Form Factor Equation:
Polar angles and ’ between normals and ray between x and y
Visibility function v(x,y) = 0 if ray from x to y is occluded, v(x,y) = 1 otherwise
Distance r between x and y
Form factors are symmetric:
Divide radiosity equation by A

12. Progressive Refinement:
Instead of computing all form-factors and then solving a complete set of linear radiosity equations, the progressive refinement method computes and distributes the light energy one patch per refinement iteration step.
Progressive refinement is a ray tracing algorithm that quickly reveals coarse structure of an image, and gradually reveals additional detail over time.
The first pixel is rendered as a single rectangle occupying the entire work area. The second through fourth each occupy a quarter of the work area.
Sufficient progression will refine the image until the rendered rectangles correspond to a target resolution
Advantage:
The main advantage of the technique from the user point of view, is to be able to quickly get a visual feedback about what the frame looks like before it is completely finished. This might be useful when an artist is tweaking the lighting or the materials of the scene.

14. Example: Screen resolution Working:
Each element in the scene maintains two energy values: an accumulated energy value and residual (or "upshot") energy. We choose one of the elements in the scene as the "shooter" .
If a receiving element is visible, then we calculate the amount of energy transferred from the shooter to the receiving element, as described by the corresponding form factor and the shooter's residual energy.
This energy is multiplied by the receiver's reflectance, which is the fraction of incoming energy that is reflected back out again, and is usually represented by an RGB color.

15. Radiosity applications:
The Radiosity method offers a powerful capability that the ray tracing technique cannot - interactive walk throughs of the environment.
dealing with diffuse reflectors in enclosures, the method works best for man-made environments such as architectural designs, interiors of offices, factories and lighting designs
useful tool for light designers and theatrical lighting designers since it accurately simulates global illumination

16. Typical features of a radiosity application for architecture would include • Translation from modeler data formats • Access to material libraries • Access to lighting libraries • Positioning of lights • Assignment of material properties • Positioning of texture maps

17. Environmental Mapping
Approximating the appearance of a reflective surface by means of a precomputed texture image
The texture is used to store the image of the distant environment surrounding the rendered object
Types:
Sphere mapping
Cube mapping
Healpix mapping

18. Steps for Environmental mapping
Create a 2D environment map Create a 2D environment map
For each pixel on a reflective object, compute the normal the normal
Compute the reflection vector based on the eye position and surface normal position and surface normal
Use the reflection vector to compute an index into the environment texture into the environment texture
Use the corresponding texture to color the pixel

19. Sphere mapping:
Represents the sphere of incident illumination as though it were seen in the reflection of a reflective sphere through an orthographic camera
a fisheye lens or via prerendering a scene is used
Synthetic scene can be generated using ray tracing

20. Cube mapping: uses the six faces of a cube as the map shape.
The environment is projected onto the sides of a cube and stored as six square textures, or unfolded into six regions of a single texture.
The cube map is generated by first rendering the scene six times from a viewpoint, with the views defined by an 90 degree view frustum representing each cube face.

21. HEALPix mapping:
HEALPix environment mapping is similar to the other polyhedron mappings, but can be hierarchical, thus providing a unified framework for generating polyhedra that better approximate the sphere. This allows lower distortion at the cost of increased computation
Healpix mapping with Grid example

22. We can display an object on a monitor screen in three different computer-model forms:
Wireframe model
Surface Model
Solid model
Wire frame model:
A wireframe model consist of points and curves only, and looks as if its made up with a bunch of wires.
This is the simplest CAD model of an object.
Advantages- 1. Ease of creation and low level hardware and software requirements. 2. the data storage requirement is low.
Disadvantage- very confusing to visualize. For example, a blind hole in a box may look like a solid cylinder, as shown in the figure.

23. Polygonal modeling: -Polygon mesh: vertex, edges and polygon collection where each edge is shared by two polygons as maximum • vertex: point with coordinates (x,y,z) • edge: line segment that joins two vertices • polygon: close sequence of edges – There are different type of representation that can be used at the same time in a same application • Explicit • Pointers to list of vertices • Pointers to list of edges – Criteria to evaluate different representations: • time • space • topological information

24. Surface detailing:
In computer graphics, the fine surface detail on an object is generated using textures.
Three aspects of texture are generally considered:
1.Texture mapping: the addition of a separately specified pattern to a smooth surface. After the pattern is added, the surface remains smooth. Also known as patterns or colour detail
2. Bump mapping: the addition of roughness to the surface. This is obtained perturbation function that changes the geometry of the surface. Also known as roughness
3. Simulating environments: for example, shadows and lighting using textures.

25. 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
We define our texture map as existing in texture space, which is a normal 2D space
The lower left corner of the image is the coordinate (0,0) and the upper right of the image is the coordinate (1,1)
The actual texture map might be 512 x 256 pixels for example, with a 24 bit color stored per pixel

26. Texture Coordinates
To render a textured triangle, we must start by assigning a texture coordinate to each vertex
A texture coordinate is a 2D point [t x t y ] in texture space that is the coordinate of the image that will get mapped to a particular vertex

27. Mapping functions: s=f(u,v) , t=g(u,v)
The mapping functions are frequently assumed to be linear:
s=A u+B
t=C v+D
where the constants A, B, C and D are obtained from the relationship between known points in the two systems.

28. Texture mapping
Image without texture
Image with texture

29. Anti-aliasing: Aliasing is a constant aspect of texture mapping
Frequency domain analysis: silhouette edges and perspective can cause high frequency patterns in image space
Point sampling (mapping the center of image pixel to texture space and use the nearest texture pixel) a texture pattern can generate lots of aliasing problems:
Wide literature on different filters to circumvent the problem

30. Bump Mapping:
A sphere without bump mapping (left). A bump map to be applied to the sphere (middle). The sphere with the bump map applied (right) appears to have a mottled surface resembling an orange. Bump maps achieve this effect by changing how an illuminated surface reacts to light without actually modifying the size or shape of the surface.

31. Bump mapping:
Adding texture patterns to smooth surfaces produces smooth surfaces
Using a rough-textured pattern to add the appearance of roughness to a surface is not a good idea. Rough-textured surfaces hava a small random component in the surface normal and hence in the light reflection direction
Blinn developed a method to for perturbing the surface normal. At any point of the surface S, the partial derivatives are Su and Sv . The surface normal n is given by the cross-product:

32. Bump Mapping:

33. Example:

34. Non- photorealistic rendering:
Non-photorealistic rendering does not reproduce the real object, but focuses on graphic art, personality and style of expression. NPR has recently become a hot research topic in computer graphics.
It produce schematic representations of scenes that include only the relevant geometric information, clarifying shapes and focusing attention

35. Algorithms in NPR: Silhouette and Hidden-Line Algorithms
Image-Space Silhouette Algorithms
Object-space silhouette algorithms
Stroke and Paint Models
Interactive Painting and Drawing
Automatic Painting Algorithms
Automatic Pen-and-Ink Algorithms

36. Applications: Architectural designs Medical textbooks In paintings
Film production industry
In animation production

37. Hatching:
Drawing surfaces using hatching strokes simultaneously conveys material, tone, and form
Hatching can simultaneously convey lighting, suggest material properties, and reveal shape.
Hatching generally refers to groups of strokes with spatially-coherent direction and quality. The density of the strokes controls tone for shading.
Their character and aggregate arrangement suggests surface texture
Several non-photorealistic rendering (NPR) methods address hatching in still images rendered from 3D scenes. However, these methods lack temporal coherence, and are thus unsuitable for animation.

38. Halftone:
Halftone is the reprographic technique that simulates continuous tone imagery through the use of dots, varying either in size or in spacing, thus generating a gradient like effect.[ "Halftone" can also be used to refer specifically to the image that is produced by this process.

39. Halftone Dot pattern:
Producing halftone dots of different sizes requires not only an appropriate halftone screen but also keeping the screen at a certain distance from a light-sensitive plate. Only then will the final dots have different sizes related to the amount of light penetrating each opening of the screen
The halftone process was used for books, newspapers, and magazines, as well as many different forms of printed and visual advertising and product decoration.
Halftone in QR scan

40. Cross hatching:
A way of adding cartoon like detail and shading to a scene.
It details a scene by adding lines right-angles to create a mesh like appearance.
In OpenGL, a rather simple shader exists to create a similar kind of scene. All we need is a fragment shader to handle the cross hatching of our scene
need a 2D texture that will tell us what fragment is being rendered and a luminace value to help determine whether or not our current fragment lies on a particular line

41. NPR techniques:
 Pen-and-Ink illustration
Techniques: cross-hatching, outlines, line art,etc.
Painterly rendering
Styles: impressionist, expressionist, pointillist, etc.
Cartoons
Effects: cartoon shading, distortion, etc.
Technical illustrations
Characteristics: Matte shading, edge lines, etc.
Scientific visualization
Methods: splatting, hedgehogs, etc.

42. Pen and ink techniques:
Strokes- Curved lines of varying thickness and density of placement
Texture - Character conveyed by collection of strokes, e.g. crisp and clean vs. rough and sketchy
Tone - Perceived gray level across the image
Outline - Boundary lines which disambiguate structure information

43. Characteristics of pen-and-ink
showing not only region borders (maybe combined w/ sparse lines)
also showing shading
also showing surface shape
also illustrating material
abstraction and emphasis
Advantages:
does not require halftoning, already black-and-white
thus images good for printing
mark placement & stylization allow abstraction & emphasis
precise depiction, good for illustration applications
high-quality representation: vector or 1 bit pixel images

44. Artistic style rendering:
Rendering in visual art and technical drawing means the process of formulating, adding color, shading, and texturing of an image
The alternative method to rendering an image is capturing an image such as photography or image scanning. Both rendered and captured images can be mixed, edited, or both
visual information is interpreted by the artist and displayed accordingly using the chosen art medium and level of abstraction in abstract art

45. Mosiacs Rendering:
Constrain camera motion to planar concentric circles, and create concentric mosaics by composing slit images taken at different locations along each circle.
Constrain cam motion to planar concentric circle, create concentric mosaics by composing slit images taken at different locations along each circle.

46. Construction of a concentric mosaic:

47. Rotoscoping:
Rotoscoping is a technique where images are copied from a moving video into an animation. The animator draws the motion and shape of the object by referring to the video as opposed to imagining in his head. With the help of the rotoscoping one can animate some complex scenes that would be hard to visualize otherwise. The disadvantage is that one will have to hunt for the exact video that one wants to animate.

48. Advantages:
Rotoscoping makes it easier to animate really difficult, complex actions.
Rotoscoping motivates students to learn more complex software applications.
The process of rotoscoping teaches students about the reality of animating as a very time intensive activity.
Things to consider:
Style: What type of drawing will you do? Experimenting in advance is encouraged to develop a style that you can consistently replicate throughout the animation
Color: You will be re-drawing the action but it does not have to be the same color. What happens when the hue is changed?
Time: This can be a very time consuming process, so do not pick a drawing style that will take you 30 minutes per frame to complete
Audio: How does the role of audio in your animation affect the style and pace?
Continuity or discontinuity in drawing style.

49. References: