Computer Creative Art Lecture 7 PDF

DM427 Lecture 7 Outline Chapter 5. Kinematic Linkages  Introduction In describing an object’s motion, it is often useful to relate it to another object. Consider, for example a coordinate system centered at our sun in which the moon’s motion must be defined. It is much easier to describe the mo...

DM427 Lecture 7 Outline Chapter 5. Kinematic Linkages  Introduction In describing an object’s motion, it is often useful to relate it to another object. Consider, for example a coordinate system centered at our sun in which the moon’s motion must be defined. It is much easier to describe the motion of the moon relative to the earth and the earth’s motion directly in a sun-centric coordinate system. Such sequences of relative motion are found not only in astronomy but also in robotics, and human figure animation.  Introduction This chapter is concerned with animating objects whose motion is relative to another object, especially when there is a sequence of objects where each object’s motion can easily be described relative to the previous one. Such an object sequence forms a motion hierarchy. Often the components of the hierarchy represent objects that are physically connected and are referred to by the term linkages.  Introduction The topics of this chapter are how to form data structures that support such linkages How to animate the linkages by specifying or determining position parameters over time.  Kinematics The branch of mechanics concerned with the motions of objects without regard to the forces that cause the motion.  Motion Hierarchy The two approaches to positioning such a hierarchy are known as forward kinematics, in which the animator must specify rotation parameters at joints, and inverse kinematics, in which the animator specifies the desired position of the hand, for example, and the system solves for the joint angles that satisfy that desire Kinematics (Forward Kinematics) Animator specifies rotation parameters at joints  Kinematics (Forward Kinematics) The Forward Kinematics takes a pose as the input, and calculates the position of the end effector as the output. With Forward Kinematics, you need to define the articulation of each joint in the articulated body. This might be fine if you have a low number of joints, but with a high number of joints this tends to be tedious!  Kinematics (Inverse Kinematics) Animator specifies the desired position of hand, and system solves for the joint angles that satisfy that desire.  Kinematics (Inverse Kinematics) This means that you know the end effector position you’d like to target, but you don’t know what the pose of the articulated body needs to be for the end effector to reach this target position. This is where Inverse Kinematics shines! With Inverse Kinematics, you do not need to define the whole pose of an articulated body —this gets calculated for your by the IK algorithm. With IK, you only need to define a position as the input.  Hierarchical Modeling (Data Structure) Hierarchical linkages can be represented by a tree-like structure – Root node – corresponds to the root object – Other nodes – located relative to the root node – A node from which no arcs extend downward is referred to as a leaf node. - When discussing two nodes of the tree connected by an arc, the one higher up the hierarchy is referred to as the parent node, and the one farther down the hierarchy is referred to as the child node.  Hierarchical Modeling (Articulated Model) Represent an articulated figure as a series of links connected by joints Hierarchical Modeling (Data Structure)  Hierarchical Modeling (Articulated Model) Graphics, is concerned primarily with Revolute joints, in which one link rotates about a fixed point of the other link. Prismatic joint, in which one link translates relative to another  Degrees of Freedom (DOF) The minimum number of coordinates required to specify completely the motion of an object. It defines the number of independent parameters that define the configuration of a mechanical system. Degrees of Freedom of a Rigid Body in Space An unrestrained rigid body in space has six degrees of freedom: three translating motions along the x, y and z axes and three rotary motions around the x, y and z axes respectively.  Degrees of Freedom (DOF) Structures in which more than one DOF are coincident are called complex joints.