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Understand how hierarchical modeling organizes objects and forward kinematics determines motion in animations. Learn about joint constraints, kinematic chains, and data structures in computer graphics.
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CSCI480/582 Lecture 12 Chap.3.1 Hierarchical Modelling and Forward Kinematics Feb, 18, 2009
Outline • Articulated motion in general • Hierarchical Modelling • Forward Kinematics
Objects of “linked” parts • A “link” is a physical connection made of • Mechanical joint with visible geometric structures • Gravity force without visible structures • Magnet Field Force • “Invisible” metal wires in Magic shows, etc. • Motions of one part is relative to its “linked” part • Which forms a Motion Hierarchy • The geometric transformation model of a linked part has reduced degree of freedom due to the constraints defined by the link
The Kinematics of Linked Objects • Data structure that supports link constraints • e.g. Human body defined by a hierarchy of rotational joints connected by rigid shapes • Determine geometric transformation model during animations • Forward kinematics: Joint rotation/translation parameters are directly specified to determine the motion • Inverse kinematics: Desired position of leaf-node parts (parts that has no linked part whose motion is relative to it) are specified, the application solves the rotation/translation parameters that meets the specifications.
Hierarchical Modelling – Basics • The enforcement of relative location constraints among objects organized in a tree • Articulation: The movements of an appendage by changing the configuration of a joint • Joint constraints: • Joint Degree of freedom (DOF): minimum number of parameters to define the motion allowed by a joint Revolute Joint Ball-and-socket Joint Presmatic Joint
Hierarchical Modeling – Data Structure • Linkage represented by a tree structure of • Nodes connected by Arcs • Contains • A constant transformation MScurr of Linkcurr relative to linkparent • A variable transformation MAcurr responsible for articulating Nodecurr • Constrains of the transformation variable Arccurr Nodecurr • Contains • Object data Root Node Abstract hierarchical representation of an articulated figure Tree structure
Draw an Articulated Model in Forward Kinematics in OpenGL • Direct display without node-arc data structure Partial code in display() glutSolidSphere( 0.5, 32, 32 ); glPushMatrix(); glRotatef( earth2sunRotate, 0.0, 1.0, 0.0 ); glTranslatef( 4.0, 0.0, 0.0 ); glPushMatrix(); glRotatef( earthSelfRotate, 0.866, 0.5, 0.0 ); glutSolidSphere( .05, 32, 32 ); glPopMatrix(); glPushMatrix(); glRotatef( moon2earthRotate,0.0, 1.0, 0.0 ); glTranslatef( 0.2, 0.0, 0.0 ); glutSolidSphere( 0.03, 32, 32 ); glPopMatrix(); glPopMatrix(); void idle() { if ( animationMode == 1 ) { earth2sunRotate += 0.5; moon2earthRotate += 6.5; earthSelfRotate += 20; glFlush(); glutPostRedisplay(); } }
Draw an Articulated Model in Forward Kinematics – Transverse The Tree Abstract Arc class Abstract Node class Class Arc { virtual void draw() { glPushMatrix() glLoadMatrix( (GLfloat*) A_ ); glPushMatrix(); glLoadMatrix( (GLfloat*)T_); node_.draw(); for( int i = 0; I < children_.size(); ++i ) children_[i].draw(); glPopMatrix(); glPopMatrix(); } Private: Arc* parent_; std::vector<Arc> children_; Node* node_; ModelMatrix T_; ModelMatrix A_; } Class Node { virtual void draw(); }; Segments of the main program /// create the hierarchical tree Std::vector<Node> nodeList; Std::vector<Arc> arcList; /// draw the tree arcList[0].draw();
