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Types of Collisions - II

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When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

Elastic Collisions: Case Study

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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

Elastic Collisions: Introduction

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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...

Types Of Collisions - I

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When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...

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Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

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Simple culling methods for continuous collision detection of deforming triangles.

Xinyu Zhang¹, Young J Kim

¹Department of Computer Engineering, Ewha Womans University, 11-1 Daehyun-Dong Seodaemun-Gu, Seoul 120-750, South Korea. zhangxy@ewha.ac.kr

IEEE Transactions on Visualization and Computer Graphics

|June 22, 2011

Summary

This summary is machine-generated.

This study introduces an efficient continuous collision detection (CCD) method for deforming triangles. The new conservative advancement approach significantly improves performance over existing algorithms.

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Area of Science:

Computer Graphics
Computational Geometry
Collision Detection

Background:

Continuous collision detection (CCD) is crucial for realistic simulations involving dynamic objects.
Existing CCD algorithms for deforming primitives can be computationally expensive.
Efficient detection of collisions between deforming triangles is a persistent challenge.

Purpose of the Study:

To develop a simple and efficient algorithm for continuous collision detection (CCD) of deforming triangles.
To improve the performance of CCD for triangle primitives in simulations.
To leverage conservative advancement for enhanced efficiency.

Main Methods:

The proposed method utilizes a conservative advancement technique.
It relies on a sequence of simple, provably collision-free conditions for deforming triangles.
The algorithm is designed for efficiency and simplicity.

Main Results:

The developed CCD algorithm demonstrates significant performance improvements.
Experimental results show a 2-30 times performance gain compared to existing methods.
The approach is effective for deforming triangle primitives.

Conclusions:

The presented approach offers a simple and efficient solution for CCD of deforming triangles.
Conservative advancement with collision-free conditions is key to the algorithm's performance.
This method provides a substantial speedup for real-time simulations requiring accurate collision handling.