![]() In three dimensions, close-packed structures offer the best lattice packing of spheres, and is believed to be the optimal of all packings. Many other shapes have received attention, including ellipsoids, Platonic and Archimedean solids including tetrahedra, tripods (unions of cubes along three positive axis-parallel rays), and unequal-sphere dimers. The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales. This problem is relevant to a number of scientific disciplines, and has received significant attention. Many of these problems, when the container size is increased in all directions, become equivalent to the problem of packing objects as densely as possible in infinite Euclidean space. In some variants the overlapping (of objects with each other and/or with the boundary of the container) is allowed but should be minimized. More commonly, the aim is to pack all the objects into as few containers as possible. In some variants, the aim is to find the configuration that packs a single container with the maximal packing density. Usually the packing must be without overlaps between goods and other goods or the container walls. ![]() The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. A set of objects, some or all of which must be packed into one or more containers.Multiple containers may be given depending on the problem. A container, usually a two- or three-dimensional convex region, possibly of infinite size.Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. Many of these problems can be related to real-life packaging, storage and transportation issues. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Lines overlap because the point is not bound the circle, which is what I'm assuming is causing the "Failed to validate broken face." When padding it.Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. I wanted the larger circle to serve as the closing face for the smaller geometry if that is possible It is the two parallel line and the semicircle. Note that it is only three lines and not a closed geometry. ![]() I managed to get the sketch fully contained, but the pad operation got the classic "Failed to validate broken face." and unless it's just representing the constraints properly, I believe it's because one of the points is not actually locked to the edge. On that line, I would like to match the two corners of a rectangular object created with the Polyline tool. So I have a circle constrained to a radius of 25.1mm. OS: Linux Mint 20.3 (X-Cinnamon/cinnamon) I'm having a little hard time with this one and I was curious what's the best way to go about containing two points on a geometry to their locations on a circle.
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