Concepts inSimple linear bending stiffness in particle systems
Bending stiffness
The bending stiffness of a beam relates the applied bending moment to the resulting deflection of the beam. It is the product of the elastic modulus of the beam material and the area moment of inertia of the beam cross-section. According to elementary beam theory, the relationship between the applied bending moment and the resulting curvature of the beam is where is the deflection of the beam and the spatial coordinate.
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Particle system
The term particle system refers to a computer graphics technique to simulate certain fuzzy phenomena, which are otherwise very hard to reproduce with conventional rendering techniques. Examples of such phenomena which are commonly replicated using particle systems include fire, explosions, smoke, moving water, sparks, falling leaves, clouds, fog, snow, dust, meteor tails, hair, fur, grass, or abstract visual effects like glowing trails, magic spells, etc.
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Spring (device)
A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication. Some non-ferrous metals are also used including phosphor bronze and titanium for parts requiring corrosion resistance and beryllium copper for springs carrying electrical current (because of its low electrical resistance).
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Force
In physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e. , to accelerate, or which can cause a flexible object to deform. Force can also be described by intuitive concepts such as a push or pull.
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Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context.
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Cloth modeling
Cloth modeling is the term used for simulating cloth within a computer program; usually in the context of 3D computer graphics. The main approaches used for this may be classified into three basic types: geometric, physical, and particle/energy.
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Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that areas above the axis add to the total, and the area below the x axis subtract from the total.
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