Computer Graphics (Fall 2005)To DoCourse OutlineSlide 4Rendering: 1960s (visibility)Rendering: 1970s (lighting)Rendering (1980s, 90s: Global Illumination)OutlineMotivationLinear Relationship of LightGeneral ConsiderationsDiffuse Lambertian TermMeaning of negative dot productsPhong Illumination ModelIdea of Phong IlluminationPhong FormulaAlternative: Half-Angle (Blinn-Phong)Slide 18Triangle Meshes as ApproximationsColoring Between the LinesFlat vs. Gouraud ShadingGouraud Shading – Details 1Gouraud Shading – Details 2Gouraud and Errors2 Phongs make a HighlightProblems with Interpolated ShadingComputer Graphics (Fall 2005)Computer Graphics (Fall 2005)COMS 4160, Lecture 16: Illumination and Shading 1http://www.cs.columbia.edu/~cs4160To DoTo DoWork on HW 3, do wellStart early on HW 4Discussion of midtermBut remember HW 3, HW 4 more importantCourse OutlineCourse Outline3D Graphics Pipeline Rendering(Creating, shading images from geometry, lighting, materials) Modeling(Creating 3D Geometry)Course OutlineCourse Outline3D Graphics Pipeline Rendering(Creating, shading images from geometry, lighting, materials) Modeling(Creating 3D Geometry)Unit 1: TransformationsWeeks 1,2. Ass 1 due Sep 22Unit 2: Spline CurvesWeeks 3,4. Ass 2 due Oct 7Unit 3: OpenGLWeeks 5-7. Ass 3 due Nov 10Midterm on units 1-3: Oct 26Unit 4: Lighting, ShadingWeeks 8,9. Written Ass 1 due Nov 16Ass 4: Interactive 3D Video Game (final project) due Dec 13Rendering: 1960s (visibility)Rendering: 1960s (visibility)Roberts (1963), Appel (1967) - hidden-line algorithmsWarnock (1969), Watkins (1970) - hidden-surface Sutherland (1974) - visibility = sortingImages from FvDFH, Pixar’s ShutterbugSlide ideas for history of Rendering courtesy Marc Levoy1970s - raster graphicsGouraud (1971) - diffuse lighting, Phong (1974) - specular lightingBlinn (1974) - curved surfaces, textureCatmull (1974) - Z-buffer hidden-surface algorithmRendering: 1970s (lighting)Rendering: 1970s (lighting)Rendering (1980s, 90s: Global Illumination)Rendering (1980s, 90s: Global Illumination) early 1980s - global illumination Whitted (1980) - ray tracingGoral, Torrance et al. (1984) radiosityKajiya (1986) - the rendering equationOutlineOutlinePreliminariesBasic diffuse and Phong shadingGouraud, Phong interpolation, smooth shadingFormal reflection equation (next lecture)Texture mapping (in one week)Global illumination (next unit)For today’s lecture, slides and chapter 9 in textbookMotivationMotivationObjects not flat color, perceive shape with appearanceMaterials interact with lightingCompute correct shading pattern based on lightingThis is not the same as shadows (separate topic)Some of today’s lecture review of last OpenGL lec.Idea is to discuss illumination, shading independ. OpenGLToday, initial hacks (1970-1980)Next lecture: formal notation and physicsLinear Relationship of LightLinear Relationship of LightLight energy is simply sum of all contributionsTerms can be calculated separately and later added together:multiple light sourcesmultiple interactions (diffuse, specular, more later)multiple colors (R-G-B, or per wavelength)kkIIGeneral ConsiderationsGeneral ConsiderationsSurfaces are described as having a position, and a normal at every point.Other vectors usedL = vector to the light sourcelight position minus surface point positionE = vector to the viewer (eye)viewer position minus surface point position(x1,y1,z1)N1(x2,y2,z2)N2Diffuse Lambertian TermDiffuse Lambertian TermRough matte (technically Lambertian) surfacesNot shiny: matte paint, unfinished wood, paper, … Light reflects equally in all directionsObey Lambert’s cosine lawNot exactly obeyed by real materialsI N L�:N-LMeaning of negative dot productsMeaning of negative dot productsIf (N dot L) is negative, then the light is behind the surface, and cannot illuminate it.If (N dot E) is negative, then the viewer is looking at the underside of the surface and cannot see it’s front-face.In both cases, I is clamped to Zero.Phong Illumination ModelPhong Illumination ModelSpecular or glossy materials: highlightsPolished floors, glossy paint, whiteboardsFor plastics highlight is color of light source (not object)For metals, highlight depends on surface colorReally, (blurred) reflections of light sourceRoughnessIdea of Phong IlluminationIdea of Phong IlluminationFind a simple way to create highlights that are view-dependent and happen at about the right placeNot physically basedUse dot product (cosine) of eye and reflection of light direction about surface normalAlternatively, dot product of half angle and normalRaise cosine lobe to some power to control sharpness or roughnessPhong FormulaPhong Formula-LRE( )pI R E: g?R =2( )R L L N N=- + gAlternative: Half-Angle (Blinn-Phong)Alternative: Half-Angle (Blinn-Phong)In practice, both diffuse and specular components for most materialsHN( )pI N H: gOutlineOutlinePreliminariesBasic diffuse and Phong shadingGouraud, Phong interpolation, smooth shadingFormal reflection equation (next lecture)Texture mapping (in one week)Global illumination (next unit)Not in text. If interested, look at FvDFH pp 736-738Triangle Meshes as ApproximationsTriangle Meshes as ApproximationsMost geometric models are large collections of triangles.Triangles have 3 vertices, each with a position, color, normal, and other parameters (such as n for Phong reflection).The triangles are an approximation to the actual surface of the object.Coloring Between the LinesColoring Between the LinesWe know how to calculate the light intensity given:surface positionnormalviewer positionlight source position (or direction)How do we shade a triangle between it’s vertices, where we aren’t given the normal?Flat vs. Gouraud ShadingFlat vs. Gouraud ShadingFlat - Determine that each face has a single normal, and color the entire face a single value, based on that normal.Gouraud – Determine the color at each vertex, using the normal at that vertex, and interpolate linearly for the pixels between the vertex locations.glShadeModel(GL_FLAT) glShadeModel(GL_SMOOTH)Gouraud Shading – Details 1Gouraud Shading – Details 1Inter-vertex interpolation can be done in object space (along the face), but it is simpler to do it in image space (along the screen).2 ways for a