We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening–straightening flow. In this paper...
I. CHOIKODAI MATH. J.39 (2016), 579–595CURVED FOLDING AND PLANAR CUTTING OFSIMPLE CLOSED CURVE ON A CONICAL ORIGAMIIkhan ChoiAbstractThe fold-and-cut theorem states that one can f i nd a f l at folding of paper, so thatone complete straight cut on the folding creates any desired po...
On physical grounds, the flux across such a curve must be equal to the incoming volume. Can we prove this result? One way of proving this is to show that the divergence theorem holds for regions bounded by fractal curves. The precise conditions under which the divergence theorem holds has ...
In this paper, we present a method based on a quadratic spline quasi-interpolant for the estimation of integral properties of a planar closed curve. The latter include the length, area, center of gravity and moment of inertia of the given curve. Then, we analyze the error estimates on the...
Proof Since recursive subdivision is a corner-cutting procedure, the limit curve must be variation diminishing with respect to the original control polygon. But by Theorem 5.11, the Bezier curve is the limit curve generated from the original control polygon by recursive subdivision, so Bezier curves...
Note, curves must be co-planar. CreateBooleanDifference(Curve curveA, IEnumerable<Curve> subtractors) Calculates the boolean difference between a closed planar curve, and a list of closed planar curves. Note, curves must be co-planar. CreateBooleanIntersection(Curve curveA, Curve curveB,Double ...
Closed curve(Boolean) - creates a closed (periodic) curve Curve reference(QLV: Mate connector) - the overall CSYS reference for the curve. If left empty the reference will be the Part Studio origin, Selected point(READ ONLY) - shows the index/ID of the current se...
In traditional model-based object recognition systems, a model of each object in the model database is matched in a random sequence against the scene image. The matching procedure must be repeated for every model in the database until a correct match is found. The major problem with such an...
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Before we can scan-convert the isoparametric curves corresponding to the surface, one must be able to evaluate the normal of the surface at each point of each curve in the coverage. Toward this end, we evaluate the unnormalized surface normal field of S, (30.5)n¯(u,v)=∂S∂u∧...