BPC: Art and Computation – Summer 2007 Computer Graphics Principles Erik Brisson

BPC: Art and Computation – Summer Computer Graphics Basic paradigm Modeling Transformations Lighting and shading Scan conversion Texture mapping Alternative rendering methods

BPC: Art and Computation – Summer C.G. paradigm with light

BPC: Art and Computation – Summer Model geometry – two cuboids

BPC: Art and Computation – Summer Model geometry - approximation

BPC: Art and Computation – Summer Math representation Vertices P1 = (4.0, 2.0) P1 = (4.0, 2.0) P2 = (2.0, 2.0) P2 = (2.0, 2.0) P3 = (2.0, 4.0) P3 = (2.0, 4.0) P4 = (4.0, 4.0) P4 = (4.0, 4.0) P5 = (6.0, 3.0) P5 = (6.0, 3.0) P6 = (4.0, 1.0) P6 = (4.0, 1.0) P7 = (7.0, 1.0) P7 = (7.0, 1.0) P8 = (8.0, 2.0) P8 = (8.0, 2.0)Faces: F1 = [P1, P2, P3, P4] F1 = [P1, P2, P3, P4] F2 = [P1, P4, P5] F2 = [P1, P4, P5] F3 = [P7, P6, P1, P5, P8] F3 = [P7, P6, P1, P5, P8]

BPC: Art and Computation – Summer Computer representation Vertices 1: 4.0, 2.0 1: 4.0, 2.0 2: 2.0, 2.0 2: 2.0, 2.0 3: 2.0, 4.0 3: 2.0, 4.0 4: 4.0, 4.0 4: 4.0, 4.0 5: 6.0, 3.0 5: 6.0, 3.0 6: 4.0, 1.0 6: 4.0, 1.0 7: 7.0, 1.0 7: 7.0, 1.0 8: 8.0, 2.0 8: 8.0, 2.0Faces: 1: 1, 2, 3, 4 1: 1, 2, 3, 4 2: 1, 4, 5 2: 1, 4, 5 3: 7, 6, 1, 5, 8 3: 7, 6, 1, 5, 8

BPC: Art and Computation – Summer Rigid body transformations

BPC: Art and Computation – Summer Composition of transformations Rotate first Then translate Translate first Then rotate

BPC: Art and Computation – Summer Other transformations - scaling

BPC: Art and Computation – Summer Objects in 3D Vertices P1 = (0.0, 0.0, 2.7) P1 = (0.0, 0.0, 2.7) P2 = (1.0, 0.0, 0.5) P2 = (1.0, 0.0, 0.5) P3 = (0.998, 0.156, 0.5) P3 = (0.998, 0.156, 0.5) P4 = (0.951, 0.309, 0.5) P4 = (0.951, 0.309, 0.5) P5 = (0.891, 0.454, 0.5) P5 = (0.891, 0.454, 0.5) …Faces: F1 = [P1, P2, P3] F1 = [P1, P2, P3] F2 = [P1, P3, P4] F2 = [P1, P3, P4] F3 = [P1, P4, P5] F3 = [P1, P4, P5] …

BPC: Art and Computation – Summer Transformations in 3D Sphere translated by translated by (-3.0, 2.0, -4.5) (-3.0, 2.0, -4.5) Blue cube translated by translated by (2.0, 0.0, -4.0) (2.0, 0.0, -4.0) rotated 60 deg rotated 60 deg around y-axis around y-axis Purple cube translated by translated by (0.0, 0.0, 0.0) (0.0, 0.0, 0.0)

BPC: Art and Computation – Summer Rotations in 3D

BPC: Art and Computation – Summer C.G. paradigm with light

BPC: Art and Computation – Summer C.G. basic calculation

BPC: Art and Computation – Summer Lighting - vectors V_eye = P_eye - P V_light = P_light - P V_eye = (4, 1, 10) - (5, 2, 3) = (-1, -1, 7) V_light = (3, 7, 2) – (5, 2, 3) = (-2, 5, -1)

BPC: Art and Computation – Summer Unit shading vectors n = surface normal vector u_light = unit vector to light point u_eye = unit vector to view point

BPC: Art and Computation – Summer Shading at vertices, interpolation

BPC: Art and Computation – Summer Flat shading vs Gouraud shading

BPC: Art and Computation – Summer Shading ambient diffuse specular

BPC: Art and Computation – Summer Ray tracing

BPC: Art and Computation – Summer Scan-conversion of polygon

BPC: Art and Computation – Summer C.G. concept - texture map

BPC: Art and Computation – Summer Texture mapping + 

BPC: Art and Computation – Summer Resulting image

BPC: Art and Computation – Summer Result is a digital image

BPC: Art and Computation – Summer The quest for photorealism

BPC: Art and Computation – Summer Alternative rendering techniques

BPC: Art and Computation – Summer Alternative rendering techniques

BPC: Art and Computation – Summer D object photography index.asp

BPC: Art and Computation – Summer Panoramic photography

BPC: Art and Computation – Summer Other techniques

BPC: Art and Computation – Summer Other techniques, laser scanning

BPC: Art and Computation – Summer Now we can model, transform, illuminate, and render doughnuts