PRESENTED BY
ONKAR KADAM
DEEP KABRA
DHAVAL JOSHI

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KINEMATICS MODELING
Meaning
This determines the location of 3D objects with respect to a world system of co-ordinates as well as their motion in the virtual world.
Object kinematics is governed by parent-child hierarchical relations, with the motion of a parent object affecting that of its child.
Kinematics modeling is the way the world is viewed.
Two interpretations of transform
Global:
An operator that “displaces” a point (or set of points) to desired location
Local:
specify where objects are placed in WCS by moving the local frame
Homogeneous Tranformation Matrix
A homogeneos tranformation matrix is given as:
Where
R3*3 rotation submatrix
P3*1 vector expressing position
Homogeneous transformation matrices offer following advatages:
It treats both rotations and translations in a uniform way.
They can be compounded ,such that complex kinematics relationships can be modeled.
Object position
The system of coordinate is attached to the object at its center.
When object moves in virtual world the co ordinates move with it.
Therefore position and orientation of the object system of co-ordinates remain invariant.
The virtual prism has an attached system of co-ordinates(i1,j1,k1)
It has origin at its centre of gravity.
Absolute position of objectis referencedto a fixed system of co-ordinates called as WCS(iw,jw,kw)
Transformation from objects co-ordinates to WCS is given by
The above matrix is fixed as long as the object is static ,but if object moves the matrix becomes function of time.
The position of any vertex Vi in the system (i1,j1,k1)is known as 3D model file of object.
Vi(t)=Tw—1(t)Vi
where i=1……n(total no of vertices).
Sometimes scaling is reqd. Operation followed
will be (1)translate (2)scaling
(3)Translated to original position
Transformation Invariants
The figure shows that same world contains a virtual ball and a virtual hand.
If virtual hand interacts with the ball then we need their relative position in the virtual world.
Eg: hand slaps the ball with the palm then we need the transformation Treceiver-ball(t)
Tracker’s relative position and orientation is given to source by time dependent HTM
T source receiver(t).
Position in WCS is given by
T w source.
Thus virtual hand can be moved in virtual world by multiplying all its vertices with a compound matrix as in:
V(T)=Tw-source *Tsource-receiver(T)*Vhand
Object Hierarchies
Groups of objects which move together as a whole ,but whose parts can also be moved independently.
2 level of object
higher level –parent
Lower level-child
Motion of parent replicated by all children.
Children can move without affecting parent’s position
Children can move without affecting parent’s position
Graphically model hierarchy represented by tree graph.
At top of tree graph stands a global transformation that determines the view to the scene.
The resulting tree graph of virtual football player is shown below:
Viewing 3D world
Graphics pipeline has following stages:
Mapping virtual objects to camera co-ordinates
Lighting
Perspective projection
Clipping
Scan mapping
It is concerned only with what camera sees.