Introduction 3 D Computer Graphics part 1 Projective

Introduction 3 D Computer Graphics part 1 Projective display Viewing pipeline Graphics hardware Image-based rendering IN 4151 Introduction 3 D graphics 1

Polygon models v 8 n v 5 v 4 z v 1 y x v 7 v 6 v 3 Vertices defined with respect to world coordinate system with x, y, z coordinates v 2 x d n o IN 4151 Introduction 3 D graphics 2

Viewing transformation t v w Eye point Center of Projection u Center of Interest z y IN 4151 Introduction 3 D graphics x 3

Perspective transformation p z y p’ q q’ COP z d x IN 4151 Introduction 3 D graphics d O x' x 4

Clipping • Clipping after perspective transformation • Take care of special cases (e. g. first remove points with negative z-coordinate) IN 4151 Introduction 3 D graphics 5

Viewport transformation ywmax zwmax ywmin yvmax zwmin xwmin Window For standard case: xwmax zdepthrange yvmin xvmax Viewport / screen IN 4151 Introduction 3 D graphics 6

Rasterization dx/dy dz/dx IN 4151 Introduction 3 D graphics • Set-up increments along the edges • Interpolate along edges and along spans • Interpolate shading, normals, texture coordinates over span 7

Hidden-surface removal Wire frame Backface removal n view Backface: IN 4151 Introduction 3 D graphics Hidden surface framebuffer depthbuffer n If (z < zdepthbuffer ) then setpixel 8

Shading Light interaction with surface is complex: – – reflects diffusely-specularly is absorbed, and partly re-emitted, changes color is transmitted, and at different position re-emitted approximations are needed IN 4151 Introduction 3 D graphics 9

Phong model L f R f N L Diffuse reflection reflects light equally into all directions V Specular reflection reflects light around reflection direction Ambient term for indirect light IN 4151 Introduction 3 D graphics 10

Reflection parameters 0. 0 0. 1 0. 3 3 6 9 0. 5 0. 7 25 200 0. 25 0. 0 0. 2 0. 4 0. 5 0. 75 0. 6 0. 8 1. 0 IN 4151 Introduction 3 D graphics 11

Gouraud shading normal at vertices are interpolated from normals of adjacent polygons faceted appearance To avoid faceted effect, calculate intensity at vertices and interpolate over facet smooth appearance I 1(x 1, y 1) Ia (xa , ys ) Is (xs , ys ) I 2 (x , y ) 2 2 Ib (xb , ys ) (x 4, y 4) I 4 I 3 (x 3, y 3) IN 4151 Introduction 3 D graphics 12

Texture mapping v y texture u object pixel screen • Texture mapping is a composed 2 D perspective transformation • Perspective projection maps “pre-image” in texture space to image space • Filtering is required IN 4151 Introduction 3 D graphics x texture screen 13

Mipmap texture map polygon in perspective projection rasterized and textured u d Mipmap is image pyramid with increasingly filtered/compressed images IN 4151 Introduction 3 D graphics v R G B G R B 14

Anti-aliasing Point sampling Area sampling Alpha blending / compositing + = d~a Special cases IN 4151 Introduction 3 D graphics 15

IN 4151 Introduction 3 D graphics 16