Hierarchical Modeling

Transcription

1 Hierarchical Modeling Modeling with Transformations You ve learned everything you need to know to make a root out of cues. Just translate, rotate, and scale each cue to get the right size, shape, position, and orientation. Looks great--until you try to make it move. 1

2 Modeling with Transformations When you want to change something, the model falls apart Reason: root is constrained, ut your model is not Need a set of parameters that make it easy to move our root through legal configurations Convenient for static models, and vital for animation! Key is to structure the transformations using a hierarchy Review: Model to World Frame 2

3 Review: Model to World Frame M = T R S In OpenGL ppropriate transformation set up from the model frame to the world frame pply it to the MODELVIEW matrix BEFORE EXECUTING the code Model à World glmatrixmode(gl_modelview); /* M = T R S */ glloadidentity ( ); gltranslatef (...); glrotatef (...); glscalef(..); glucylinder (...) /* or other symol */ 3

4 Model à World Scenario Position and orient the root hammer in the world space: upper arm lower arm ase hammer solute Transformations Each part of the oject is transformed independently relative to the origin: Translate ase y (5,0,0) Translate lower arm y (5,0,0) Translate upper arm y (5,0,0) Translate hammer y (5,0,0) 4

5 Relative Transformations Better: Transform each oject relative to its parent. Step 1: Translate ase and its descendants y (5,0,0) Relative Transformations Step 2: Rotate lower arm and its descendants y -90 degrees aout local y axis 5

6 Hierarchical Transforms Hierarchical Transforms with OpenGL Translate ase and all its descendants y (5,0,0) Rotate lower arm and descendants y -90 degrees aout local y glmatrixmode(gl_modelview); glloadidentity(); gltranslatef(5,0,0); Draw_ase(); glrotatef(-90, 0, 1, 0); Draw_lower _arm(); Draw_upper_arm(); Draw_hammer(); 6

7 rticulated Models Rigid parts connected y joints [Demo 3D Root] By modeling joint angles, you can do animations Question is, given all the join angles, how do you draw the model? Making an rticulated rm a c B minimal 2D jointed oject: Two pieces, ( forearm ) and B ( upper arm ) ttach point c on B to point a on ( elow ) Desired parameters: shoulder position S (point at which winds up) shoulder angle β ( and B rotate together aout ) elow angle α ( rotates aout a = c) 7

8 Making an rm, step 1 a want a Start with and B in their untransformed configurations (B is hiding ehind ) First apply a series of transformations to, leaving B where it is Making an rm, step 2 Translate y -a, ringing a to the origin a a B You can now see B peeking out from ehind 8

9 Making an rm, step 3 Next, we rotate y the elow angle α B B a a c Making an rm, step 4 Translate to to form the elow joint at c a B c a B c 9

10 Making an rm, step 5 From now on, each transformation applies to oth and B (This is important!) Translate y -a, ringing a to the origin and B move together, so the elow doesn t separate! a B c a B c Making an rm, step 6 Next, rotate y the shoulder angle -β again, and B rotate together a B c 10

11 Making an rm, last step Finally, translate y the shoulder position S, ringing the arm where we want it S= Note that S, α, and β are parameters of the model But a,, and c are structural constants. Changing S, α, or β wiggles the arm Changing a,, or c dismemers it (useful only in video games!) 11

12 Hierarchical Transforms T S R - β T - Upper arm B T c R α T - a pply all the way down Lower rm pply all the way down Hierarchical Transforms in OpenGL T S R - β T - Upper arm B T c R α T - a Lower rm Down edges: Push, transform, draw Up edges: Pop glloadidentity(); glpushmatrix(); glpushmatrix(); glpopmatrix(); glpopmatrix(); 12

13 rticulated Model Exercise rlculated model rigid parts connected y joints Given x, y, α, β, θ 1 and θ 2, draw the scooter. Step 1 Write functions that draw parts in default location: DrawBody DrawHandle DrawWheel DrawBrake

14 Step 2 Construct the scene graph (model as a tree) 5 40 Body Handle Back Wheel Front Wheel Lower Brake Upper Brake Step 3 Lael each edge with transformalon necessary to posilon child with respect to parent, in parent s default localon Body (transform handle w.r.t. default ody) Handle Back Wheel Front Wheel Lower Brake (transform reak w.r.t. default handle) Upper Brake 14

15 Tree Laeling Step T x,y Body T 30,20 R -α Handle Back Wheel T -30 R β T 30 R β Front Wheel T -35 R θ1 Lower Brake T -35 R θ2 Upper Brake glpushmatrix(); gltranslatef(x, y); DrawBody(); Step 3 Code it up: glmatrixmode(gl_modelview); Handle Back Wheel T -35 R θ1 T -35 R -θ2 Lower Brake T 30,20 R -α Upper Brake T x,y Body T -30 R β T 30 R β Front Wheel Down edges: Push, transform, draw. Up edges: Pop. 15

16 Back to the Root Root Guy l-- left r-- right -u- upper rua lla lua -l- --a --l lower arm leg rla rul lul lll rll 16

17 Step 1 Write functions that draw parts in default location head(); h=3, w=2 right_upper_arm(); h=1, w=3 right_lower_arm(); h=1, w=2 lea_upper_arm(); h=1, w=3 torso(); h=5, w=2 lea_lower_arm(); h=1, w=2 lea_upper_leg(); right_upper_leg(); h=3, w=1 lea_lower_leg(); right_lower_leg(); h=2, w=1 Step 2 Scene Graph (Tree) (posilon in the scene) T x,y Torso 17

18 Step 3 Code it up: glmatrixmode(gl_modelview); glpushmatrix(); gltranslatef(x, y); torso(); Hands-on Session Download rootskeleton.cpp from class wesite Complete Steps 1, 2, 3 to draw the root dd a menu that allows selection of individual joints (see viewport.cpp for menu code) dd a (+/-) keyoard listener to cause the selected joint angle to increase/decrease dd a special key listener to enale arrows to move the root (see events.cpp for listener) dd Idle or Timer events to make the root dance 18