Computer Graphics (CS 543) Lecture 4a: Introduction to Transformations

Transcription

1 Coputer Graphics (CS 543) Lecture 4a: Introduction to Transforations Prof Eanuel Agu Coputer Science Dept. Worcester Polytechnic Institute (WPI)

2 Hidden-Surface Reoval If ultiple surfaces overlap, we want to see only closest OpenGL uses hidden-surface technique called the z-buffer algorith Z-buffer copares objects distances fro viewer (depth) to deterine closer objects If overlap, Draw face A (front face) Do not draw faces B and C

3 Using OpenGL s z-buffer algorith Z-buffer uses an etra buffer, (the z-buffer), to store depth inforation, copare distance fro viewer 3 steps to set up Z-buffer:. In ain( ) function glutinitdisplaymode(glut_single GLUT_RGB GLUT_DEPTH) 2. Enabled in init( ) function glenable(gl_depth_test) 3. Clear depth buffer whenever we clear screen glclear(gl_color_buffer_bit DEPTH_BUFFER_BIT)

4 3D Mesh file forats 3D eshes usually stored in 3D file forat Forat defines how vertices, edges, and faces are declared Over 4 different file forats Polygon File Forat (PLY) used a lot in graphics Originally PLY was used to store 3D files fro 3D scanner We will use PLY files in this class

5 Saple PLY File ply forat ascii. coent this is a siple file obj_info any data, in one line of free for tet eleent verte 3 property float property float y property float z eleent face property list uchar int verte_indices end_header - 3 2

6 Georgia Tech Large Models Archive

7 Stanford 3D Scanning Repository Lucy: 28 illion faces Happy Buddha: 9 illion faces

8 Introduction to Transforations May also want to transfor objects by changing its: Position (translation) Size (scaling) Orientation (rotation) Shapes (shear)

9 Translation Move each verte by sae distance d = (d, d y, d z ) object translation: every point displaced by sae vector

10 Scaling Epand or contract along each ais (fied point of origin) =s y =s y y z =s z z where p =Sp S = S(s, s y, s z )

11 Introduction to Transforations We can transfor (translation, scaling, rotation, shearing, etc) object by applying atri ultiplications to object vertices Transfored Verte P ' Py ' P ' z Transfor Matri P Py P z Original Verte Note: point (,y,z) needs to be represented as (,y,z,), also called Hoogeneous coordinates

12 Why Matrices? Multiple transfor atrices can be pre-ultiplied One final resulting atri applied (efficient!) For eaple: transfor transfor 2 transfor 3. Q Q Q y z P Py Pz Transfored Point Transfor Matrices can Be pre-ultiplied Original Point

13 3D Translation Eaple Eaple: If we translate a point (2,2,2) by displaceent (2,4,6), new location of point is (4,6,8) object Translation of object Translate(2,4,6) Translation Matri Original point Translated point Translate : = 4 Translate y: = 6 Translate z: = 4 Using atri ultiplication for translation

14 3D Translation Translate object = Move each verte by sae distance d = (d, d y, d z ) object Translation of object ' ' ' z y z y d d d z y * Where: = + d y = y + dy z = z + dz Translate(d,dy,dz) Translation Matri

15 Scaling Eaple If we scale a point (2,4,6) by scaling factor (.5,.5,.5) Scaled point position = (, 2, 3) Scale Matri for Scale(.5,.5,.5) Scale : 2.5 = Scale y: 4.5 = 2 Scale z: 6.5 = 3

16 Scaling =s y =s y y z =s z z Scale object = Move each object verte by scale factor S = (S, S y, S z ) Epand or contract along each ais (relative to origin) ' ' ' z y S S S z y z y Scale(S,Sy,Sz) Scale Matri Using atri ultiplication for scaling

17 Shearing Y coordinates are unaffected, but cordinates are translated linearly with y That is: y = y = + y * h y h y h is fraction of y to be added to (,y) ( + y*h, y) y*h

18 3D Shear

19 Reflection corresponds to negative scale factors original s = - s y = s = - s y = - s = s y = - z y S S S

20 References Angel and Shreiner, Chapter 3 Hill and Kelley, Chapter 5