Computer Graphics (CS 543) Computer Graphics (CS 543) Lecture 7 (Part - PowerPoint PPT Presentation

Computer Graphics (CS 543) Computer Graphics (CS 543) Lecture 7 (Part 3): Hierarchical 3D Models Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI)

I Instance Transformation t T f ti  Start with unique object (a symbol )  Start with unique object (a symbol )  Each appearance of object in model is an instance  Must scale, orient, position l  Defines instance transformation Instance Symbol

S Symbol ‐ Instance Table b l I t T bl Can store a model by assigning number to each Can store a model by assigning number to each symbol and storing parameters for instance transformation

R l ti Relationships in Car Model hi i C M d l  Symbol instance table does not show  Symbol ‐ instance table does not show relationships between parts of model  Consider model of car  Consider model of car  Chassis (body) + 4 identical wheels  Two symbols y  Relationship: Rate of forward motion determined by rotational speed of wheels

Structure using Function Calls St t i F ti C ll car(speed) car(speed) { chassis() wheel(right_front); ( ) wheel(left_front); wheel(right rear); g _ wheel(left_rear); }  Fails to show relationships well  Look at problem using a graph p g g p 5

G Graphs h  Set of nodes and edges (links)  Set of nodes and edges (links)  Edge connects a pair of nodes  Directed or undirected d d d  Cycle : directed path that is a loop loop loop 6

Tree  Graph in which each node (except the root) has  Graph in which each node (except the root) has exactly one parent node  May have multiple children  May have multiple children  Leaf or terminal node: no children root node root node leaf node 7

Tree Model of Car M d l f C 8 T

Hi Hierarchical Transforms hi l T f  Robot arm: Many small parts  Robot arm: Many small parts  Attributes (position, orientation, etc) depend on each other each other hammer A Robot Hammer! lower arm base

Hi Hierarchical Transforms hi l T f  Object dependency description using tree  Object dependency description using tree structure Root node Root node Base Base Object position and orientation can be affected by its parent, grand-parent, grand-grand-parent Lower arm … nodes d Upper arm Hierarchical representation is known as Scene Graph Leaf node Hammer

T Transformations f ti  Two ways to specify transformations:  Two ways to specify transformations:  (1) Absolute transformation: each part of the object is transformed independently relative to the origin transformed independently relative to the origin Translate the base by (5,0,0); Translate the lower arm by (5,0,0); Translate the upper arm by (5,0,0); y … x z

R l ti Relative Transformation T f ti A better (and easier) way: A better (and easier) way: (2) Relative transformation: Specify the transformation for each object relative to its parent for each object relative to its parent Step 1: Translate base and p its descendants by (5,0,0);

R l ti Relative Transformation T f ti Step 2: Rotate the lower arm and all its descendants relative to the base’s local y axis by -90 degree y y g y y z x x z

R l ti Relative Transformation T f ti  Represent relative transformation using scene  Represent relative transformation using scene graph Base Base T Translate (5,0,0) l t (5 0 0) Lower arm Rotate (-90) about its local y Upper arm Apply all the way pp y y down Apply all the way Hammer down

Hi Hierarchical Transforms Using OpenGL hi l T f U i O GL  Translate base and all its descendants by (5 0 0)  Translate base and all its descendants by (5,0,0)  Rotate lower arm and its descendants by ‐ 90 degree about local y ctm = LoadIdentity(); y(); Base … // setup your camera ctm = ctm * Translatef(5 0 0); ctm = ctm * Translatef(5,0,0); Lower arm Draw_base(); U Upper arm ctm = ctm * Rotatef(-90, 0, 1, 0); Draw_lower _arm(); Hammer Hammer Draw upper arm(); Draw_upper_arm(); Draw_hammer();

Hi Hierarchical Modeling hi l M d li  Previous CTM had 1 level P i CTM h d 1 l l  Hierarchical modeling: extend CTM to stack with multiple levels using linked list multiple levels using linked list     1 1 0 0 0 0 0 0     Current top 0 2 0 0   Of CTM stack 0 0 3 0           0 0 0 0 0 0 1 1

P PushMatrix hM t i  PushMatrix( ): Save current modelview matrix in stack ( )  Positions 1 & 2 in linked list are same after PushMatrix  Further Rotate, Scale, Translate affect only top matrix , , y p Before PushMatrix After PushMatrix         1 0 0 0 1 0 0 0           Current top   Current top 0 2 0 0 0 2 0 0     Of CTM stack Of CTM stack 0 0 3 0 0 0 3 0                 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1   1 0 0 0       0 0 2 2 0 0 0 0   0 0 3 0       0 0 0 1

P PopMatrix M t i  PopMatrix( ): Delete position 1 matrix, position 2 matrix p p p becomes top After PopMatrix Before PopMatrix     1 0 0 0 1 5 4 0           C Current top t t     0 0 2 2 0 0 0 0 0 2 2 0 Current top     Of CTM stack 0 0 3 0 Of CTM stack 0 6 3 0           0 0 0 1   0 0 0 1   1 0 0 0       0 2 0 0   0 0 3 0       0 0 0 1

P PopMatrix and PushMatrix Illustration M i d P hM i Ill i • Note: Diagram uses old glTranslate, glScale etc commands glScale, etc commands • We want same behavior though Ref: Computer Graphics Ref: Computer Graphics Through OpenGL by Guha

Humanoid Figure id Fi 20 H

B ildi Building the Model th M d l  Can build model using simple shapes  Can build model using simple shapes  Access parts through functions  torso() ()  left_upper_arm()  Matrices describe position of node with respect d b f d h to its parent  M lla positions left lower leg with respect to left upper l f l l h l f arm 21

Tree with Matrices ith M t i 22 T

T Tree with Matrices ith M t i Set model-view matrix to Set model-view matrix to M and draw torso 23

T Tree with Matrices ith M t i Set model-view matrix to Set model-view matrix to MM h and draw head 24

T Tree with Matrices ith M t i Set model-view matrix to Set model-view matrix to MM lua and draw left-upper arm 25

St Stack ‐ based Traversal k b d T l  We can use stack Push Pop for this  We can use stack, Push, Pop for this  Rather than recomputing MM lua from scratch or using an inverse matrix we can use the or using an inverse matrix, we can use the matrix stack to store M and other matrices as we traverse the tree we traverse the tree 26

T Traversal Code l C d save present model view matrix save present model-view matrix figure() { figure() { PushMatrix() update model-view matrix for head torso(); Rotate (…); recover original model-view matrix head(); PopMatrix(); PopMatrix(); save it again sa e it again PushMatrix(); update model-view matrix Translate(…); for left upper arm for left upper arm Rotate(…); ( ) left_upper_arm(); recover and save original PopMatrix(); p (); model-view matrix again model-view matrix again PushMatrix(); rest of code 27

VRML VRML  Scene graph introduced by SGI Open Inventor  Scene graph introduced by SGI Open Inventor  Want to have a scene graph that can be used over the World Wide Web th W ld Wid W b  Need links to other sites to support distributed d t b data bases  Virtual Reality Markup Language  Based on Inventor data base  Implemented with OpenGL 28

VRML W VRML World Example ld E l

References  Angel and Shreiner, Interactive Computer Graphics (6 th edition), Chapter 8