Collision detection for moving polyhedra.

Area of Science:

• Robotics
• Computational Geometry
• Computer-Aided Design

Background:

• Collision detection is crucial for robotics and simulations.
• Traditional methods use Euler angles, leading to complex trigonometric constraints.
• Existing methods struggle with efficient computation for moving objects.

Purpose of the Study:

• To develop a more efficient collision detection method for 3D objects.
• To simplify the mathematical representation of object-obstacle constraints.
• To enable exact intersection testing for translating and rotating objects.

Main Methods:

• Representing object rotation using quaternions instead of Euler angles.
• Deriving purely algebraic constraints in a seven-dimensional space.
• Projecting constraints into a six-dimensional configuration space.

Main Results:

• Quaternion representation transforms trigonometric constraints into algebraic ones.
• The algebraic form simplifies the computation of collision points.
• An efficient exact intersection test was derived for combined translation and rotation.

Conclusions:

• Quaternion-based algebraic constraints offer a significant advantage for collision detection.
• The proposed method enhances computational efficiency and accuracy.
• This approach is applicable to complex scenarios involving moving polyhedral obstacles.