2. COMPUTER GRAPHICS CS 482 – FALL 2014 AUGUST 27, 2014 FIXED-FUNCTION 3D GRAPHICS MESH SPECIFICATION LIGHTING SPECIFICATION REFLECTION SHADING HIERARCHICAL MODELING

3. MESH SPECIFICATION CS 482 – FALL 2014 POLYHEDRAL MESHES AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 42 MOST 3D MODELS ARE STORED AS 3D MESHES OF VERTICES, EDGES, AND FACES. VERTICES ARE USUALLY TRIPLES OF CARTESIAN COORDINATES. EDGES ARE USUALLY PAIRS OF VERTICES. FACES ARE USUALLY CYCLES OF VERTICES OR EDGES. AS MESHES BECOME MORE REFINED, WITH A LARGER NUMBER OF SMALLER FACES, THE MODEL APPROXIMATES SMOOTHER CONTOURS WITH MORE DETAILED FEATURES.

4. LIGHTING SPECIFICATION CS 482 – FALL 2014 LIGHT SOURCES AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 43 MODELING DIFFERENT LIGHT SOURCES IN A SCENE MAY PRODUCE DIFFERENT LEVELS OF LIGHTING VARIATION, RESULTING IN DIFFERENT LEVELS OF REALISM. NEARBY POINT LIGHT SOURCE DISTANT POINT LIGHT SOURCE CYLINDRICAL SPOT LIGHT CONICAL SPOT LIGHT AREA LIGHT PARALLEL LIGHT

5. LIGHTING SPECIFICATION CS 482 – FALL 2014 COMPLEXITY OF ILLUMINATION MODELS AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 44 NUMEROUS CONSIDERATIONS FACTOR INTO EFFECTIVELY LIGHTING A MODEL: HOW DOES THE LIGHT STRIKE THE OBJECT? WHAT MATERIAL PROPERTIES DOES THE OBJECT HAVE? ARE THE ITEMS BETWEEN THE OBJECT AND THE VIEWER TRANSPARENT? IF SO, WHAT REFRACTIVE QUALITIES DO THEY HAVE? IS THE OBJECT REFLECTIVE? IF SO, WHAT NEIGHBORING ITEMS REFLECT OFF THE SURFACE OF THE OBJECT? DO ANY ITEMS CAST SHADOWS ACROSS THE OBJECT? ARE ANY NEIGHBORING ITEMS SO BRIGHTLY COLORED THAT THE LIGHTING CAUSES THEIR COLORS TO “BLEED” ONTO THE OBJECT?

6. REFLECTION CS 482 – FALL 2014 AMBIENT REFLECTION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 45 TO AVOID HAVING THE PARTS OF AN OBJECT FACING AWAY FROM A LIGHT SOURCE APPEARING COMPLETELY BLACK, IT IS NECESSARY TO MODEL AMBIENT REFLECTION, LIKE THE LIGHT THAT IS SCATTERED BACK ONTO THE OBJECT FROM ITS SURROUNDINGS. WHERE I a IS THE INTENSITY OF THE AMBIENT LIGHT (ASSUMED TO BE CONSTANT FOR ALL OBJECTS), AND k a IS THE AMBIENT REFLECTION COEFFICIENT FOR THE PARTICULAR MATERIAL OF EACH OBJECT. IMAGE WITH AMBIENT REFLECTION ONLY THE EQUATION FOR THE ILLUMINATION DUE TO AMBIENT LIGHT MAY BE APPROXIMATED AS:

7. REFLECTION CS 482 – FALL 2014 DIFFUSE REFLECTION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 46 TO ILLUMINATE AN OBJECT SO THAT ITS BRIGHTNESS VARIES ACCORDING TO THE DIRECTION OF THE LIGHT SOURCE, WE CAN MODEL DIFFUSE REFLECTION, USING , THE ANGLE BETWEEN THE NORMAL VECTOR TO THE SURFACE AND THE VECTOR FROM THE SURFACE TO THE LIGHT, AS A PARAMETER. WHERE I p IS THE INTENSITY OF THE LIGHT SOURCE (ASSUMED TO BE CONSTANT FOR ALL OBJECTS), AND k d IS THE DIFFUSE REFLECTION COEFFICIENT FOR THE PARTICULAR MATERIAL OF EACH OBJECT. IMAGE WITH DIFFUSE REFLECTION ONLY THE EQUATION FOR THE ILLUMINATION DUE TO DIFFUSE REFLECTION MAY BE APPROXIMATED AS:

8. REFLECTION CS 482 – FALL 2014 COMBINING AMBIENT AND DIFFUSE REFLECTION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 47 DRAMATICALLY DIFFERENT IMAGES ARE PRODUCED BY COMBINING AMBIENT ILLUMINATION WITH DIFFUSE REFLECTION, USING THE FORMULA: HIGH DIFFUSE/LOW AMBIENT HIGH DIFFUSE/MED. AMBIENT MED. DIFFUSE/MED. AMBIENT HIGH DIFFUSE/HIGH AMBIENT LOW DIFFUSE/LOW AMBIENT

9. REFLECTION CS 482 – FALL 2014 SPECULAR REFLECTION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 48 UNTIL NOW, OUR ILLUMINATION MODEL IS NOT AFFECTED BY THE VIEWER’S POSITION. THIS CHANGES WHEN WE CONSIDER SPECULAR REFLECTION, THE DEGREE TO WHICH THE OBJECT’S SHINY SURFACE REFLECTS LIGHT INTO THE VIEWER’S EYES. WHERE k s IS THE SPECULAR REFLECTION COEFFICIENT FOR THE PARTICULAR MATERIAL OF EACH OBJECT, n IS THE SPECULAR REFLECTION EXPONENT (WHICH INDICATES HOW FOCUSED REFLECTED HIGHLIGHTS ARE ON EACH OBJECT’S SURFACE), AND  IS THE ANGLE BETWEEN THE LIGHT’S REFLECTION VECTOR OFF OF THE SURFACE AND THE VECTOR FROM THE SURFACE TO THE VIEWER. IMAGE WITH SPECULAR REFLECTION ONLY THE SPECULAR REFLECTION FORMULA IS:

10. REFLECTION CS 482 – FALL 2014 EFFECTS OF SPECULAR COEFFICIENT AND EXPONENT AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 49 INCREASING SPECULAR EXPONENT INCREASING SPECULAR COEFFICIENT NOTICE THE SMALLER “HOT SPOTS” ON THE SHINIER OBJECTS.

11. REFLECTION CS 482 – FALL 2014 LIGHT SOURCE ATTENUATION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 50 THE ILLUMINATION MODEL DOESN’T HANDLE ATTENUATION, THE TENDENCY FOR ILLUMINATION TO DISSIPATE WITH THE DISTANCE FROM THE LIGHT SOURCE. AN ATTENUATION FACTOR, f att, CAN BE INSERTED INTO THE FORMULA AS FOLLOWS: QUADRATIC/NEA R QUADRATIC/FAR LINEAR/FARLINEAR/NEARCONSTANT QUADRATIC/MEDIU M LINEAR/MEDIUM f att IS USUALLY CONSTANT, INVERSE LINEAR IN THE DISTANCE FROM THE LIGHT, OR INVERSE QUADRATIC IN THE DISTANCE FROM THE LIGHT.

12. SHADING CS 482 – FALL 2014 FLAT SHADING AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 51 BY APPLYING THE ILLUMINATION MODEL TO A SINGLE POINT WITHIN EACH POLYGONAL SURFACE AND THEN USING THAT SHADING ACROSS THE ENTIRE POLYGON, THE SURFACE OF THE MODEL RETAINS ITS FACETED APPEARANCE. NOTE THAT THE MODEL APPEARS SMOOTHER AS THE NUMBER OF POLYGONS INCREASES AND THEIR SIZE DECREASES.

13. SHADING CS 482 – FALL 2014 GOURAUD SHADING AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 52 THE GOURAUD SMOOTH SHADING ALGORITHM: CALCULATES AVERAGE VERTEX NORMAL VECTORS. PERFORMS ILLUMINATION CALCULATION TO GET VERTEX COLORS. INTERPOLATES VERTEX COLORS ACROSS EACH POLYGONAL FACE. TENDS TO SUFFER FROM MACH BANDING. MAY MISS HIGHLIGHTS WITHIN A POLYGONAL FACE. OUR ILLUMINATION MODEL PERMITS US TO SHADE OBJECTS IF WE KNOW THE SCENE’S LIGHTING CONDITIONS, THE OBJECTS’ MATERIAL PROPERTIES AND LOCATION, AND (MOST DIFFICULT OF ALL) NORMAL VECTORS AT EVERY POINT ON THE OBJECT.

14. SHADING CS 482 – FALL 2014 GOURAUD SHADING ALGORITHM AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 53 APPROXIMATE THE NORMAL VECTOR AT EACH VERTEX BY AVERAGING THE NORMAL VECTORS AT EACH FACE CONTAINING THAT VERTEX. COMPUTE THE SHADING AT EACH VERTEX USING THE ILLUMINATION MODEL. FOR EACH SCANLINE, INTERPOLATE THE SHADING FOR THE ENDPOINTS BY USING THE CALCULATED SHADING FOR THE VERTICES. THEN INTERPOLATE THE SHADING FOR THE INTERNAL SCANLINE POINTS BY USING THE ENDPOINT SHADING VALUES. CONTINUE THIS PROCESS FOR THE ENTIRE FACE.

15. SHADING CS 482 – FALL 2014 PHONG SHADING AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 54 THE PHONG SMOOTH SHADING ALGORITHM: CALCULATES AVERAGE VERTEX NORMAL VECTORS. INTERPOLATES VERTEX NORMAL VECTORS ACROSS THE FACE. PERFORMS ILLUMINATION CALCULATION AT EACH PIXEL. PRODUCES MORE ACCURATE HIGHLIGHTS. YIELDS FEWER MACH BAND EFFECTS.

16. SHADING CS 482 – FALL 2014 PHONG SHADING ALGORITHM AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 55 APPROXIMATE THE NORMAL VECTOR AT EACH VERTEX BY AVERAGING THE NORMAL VECTORS AT EACH FACE CONTAINING THAT VERTEX. FOR EACH SCANLINE, INTERPOLATE THE NORMAL VECTOR FOR THE ENDPOINTS BY USING THE NORMAL VECTOR APPROXIMATIONS FOR THE VERTICES. THEN INTERPOLATE THE NORMAL VECTORS FOR THE INTERNAL SCANLINE POINTS BY USING THE ENDPOINT NORMAL VECTORS. CONTINUE THIS PROCESS FOR THE ENTIRE FACE. USE THE ILLUMINATION MODEL TO COMPUTE THE SHADING AT EACH POINT IN THE FACE.

17. HIERARCHICAL MODELING CS 482 – FALL 2014 SCENE REPRESENTATION AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 56 A GRAPHICAL MODEL CAN BE REPRESENTED AS A LIST OF OBJECTS, BUT EDITING (E.G., DELETING) WOULD REQUIRE UPDATING MULTIPLE NODES IN THE LIST. GROUPING RELATED OBJECTS IN A MODULAR HIERARCHY FACILITATES EDITING HIGH-LEVEL EDITING VIA A SINGLE NODE.

18. HIERARCHICAL MODELING CS 482 – FALL 2014 SCENE GRAPHS AUGUST 27, 2014: FIXED-FUNCTION 3D GRAPHICSPAGE 57 A SCENE GRAPH IS A HIERARCHICAL ORDERING OF THE COMPONENTS OF A GRAPHICAL SCENE SO THAT PARENT NODES AFFECT CHILD NODES. BY ORGANIZING THE GRAPHICAL COMPONENTS IN THIS MANNER, MODELING THE BEHAVIOR OF SECONDARY COMPONENTS IS LESS COMPLICATED, SINCE CERTAIN ASPECTS OF THAT BEHAVIOR ARE ESSENTIALLY INHERITED FROM THE CORRESPONDING PRIMARY COMPONENTS.