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Torsion is a twisting force that rotates a material, the layout of a city by deciding what type of like screwing in a bolt into a piece of wood or building go where opening a jar of peanut butter b.
Building codes are a set of standards or rules d. Shear is a cutting force that pushes a material in established and enforced by local government to opposite directions, like scissors cutting paper or ensure that the structures we use are safe shaving 3.
What is Bernoullis principle? Construction Technology Problems: a.
Bernoullis principle states that as fluids like 1. A pickup truck fully loaded with cargo weighs lb.
If liquids and gases move faster their pressure the cargo weighs lb. What happens if we want to apply the smoothing to a whole scene composed of several objects? If we apply any of the proposed schemes to each object independently and then merge the results, there is no guarantee that the images of two disjoint objects will be disjoint.
More generally, little attention has been paid to global topological properties of smoothing procedures. Even when applied to a single object, there is no formal proof that known smoothing schemes preserve the objects topological characteristics number of connected components and cavities, number of tunnels in 3D , with the remarkable exception of a result concerning the evolution of a 2D plane curve under the heat equation which has been proved to shrink towards one point.
Here, objects are defined as sets of grid points, and topology preservation is ensured by the exclusive use of homotopic transformations defined in the framework of digital topology.
The homotopic alternating sequential filter is a composition of homotopic cuttings and fillings by balls of increasing radius. In particular, we consider only morphological operators based on structuring elements which are balls in the sense of the Euclidean distance, in order to obtain the desired smoothing effect.
We denote by Z the set of relative integers, and by E the discrete plane Z2. A point x E is defined by x1 , x2 with xi Z. We denote by Br the map which associates to each x in E the ball Br x.
Unless explicitly stated, the choice of the Euclidean distance will be assumed. The ball Br is termed as the structuring element of the dilation. Notice that opening and closing are dual to each other, like erosion and dilation. Also, the closing operator r is increasing, extensive X E, X r X , and idempotent.
Let us now recall the notion of medial axis see also17, A ball Br x X is maximal for X if it is not strictly included in any other ball included in X. Alternating sequential filters were introduced by Sternberg14 and were extensively studied by Serra. In most cases, applying the same alternating sequential filter to the complementary of the object would give approximately the same result up to the complementation.