3D Polygon Rendering Pipeline 원본 – ( Thomas Funkhouser (Princeton University) C0S 426 고려대학교 그래픽스 연구실 민성환

Basis 3D Plolygon rendering –3 차원으로 모델링 된 물체의 형상에 대해 색 감, 질감, 그림자, 빛의 반사 및 굴절 효과등 을 부여하는 과정 Pipeline – 하나의 process( 작업 ) 을 서로 다른 기능을 가진 여러 개의 subprocess 로 나누어 각 프 로세서가 동시에 서로 다른 데이터 처리

3D polygon rendering Many applicatons use rendering of 3d polygons with direct illumination

3d polygon rendering (cont) What steps are necessary to utilize spatial coherence while drawing these polygons into a 2D image?

3d Rendering Pipeline This is a pipelined sequence of operations to draw a 3D primitive into a 2D image For direct illumination

Example OpenGL executes steps of 3D rendering pipeline for each polygon. glBegin(GL_POLYGON) glVertex3f(0.0,0.0,0.0); … glEnd();

In Pipeline Transform into3d world coordinate system

In Pipeline Illuminate according to lighting and reflectance

In Pipeline Transform into 3D camera coordinate system

In Pipeline Transform into 2D camera coordinate system

In Pipeline Clip primitives outside camera ’ s view

In Pipeline Draw pixels

In Pipeline Transform

Transformations

Transformations review Transformations map points from one coordinate system to another

Viewing Transformations Viewing transformations

Viewing Transformation 1.Translate the view reference point to the origin of the world-coordinate system 2.Apply rotations to align the axes with the world axes,respectively

Projection General definition –Transform points in n-space to m-space(m<n) In computer graphics –Map 3D camera coordinates to 2D screen coordinates

Taxonomy of Projections

Parallel Projection Center of projection is at infinity –Direction of projection (DOP) same for all points

Orthographic Projections DOP perpendicular to view plane

Oblique Projections DOP not perpendicular to view plane

Parallel Projection Matrix General parallel projection transformation z Where L1 is the inverse of tanα,which is also the value of L when z=1

Parallel Projection Matrix General parallel projection transformation z

Taxonomy of Projections

Perspective Projection Map points onto “ view plane ” along “ projectors ” emanating from “ center of projection ” (cop)

Perspective Projetion How many vanishing point?

Perspective Projection View Volume

Perspective Projection Compute 2D coordinates from 3D coordinates with similar triangles

Perspective Projection (Cont)

Perspective Projection Matrix 4x4 matrix representation?

Perspective Projection Matrix 4x4 matrix representation?

Perspective Vs. Parallel Perspective projection – Size varies inversely with distance – looks realistic –Distance and angles are not(in general) preserved –Parallel line do not (in general) remain parallel Parallel projection –Good for exact measurements –Parallel lines remain parallel –Angles are not (in general) preserved –Less realistic looking