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It means that if you have millions of geometric entities, but few constraints, the system will be resolved fast. That accounts for number of geometric elements (n), but what about number of constraints (m)?Ī: In Cheetah the number of arithmetic operations that is required to resolve system of equations is O(m), i.e., proportional to the number of constraints. Q: You say that you have O(n) memory and computational efficiency.
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The tricky part is how to choose these groups and how to coordinate data exchange between them – we use the iterative approach for that. Each subsystem has fixed requirements for memory and computation. Q: On your website, you say other solvers solve equations in the wrong manner, “using archaic numeric methods” (e.g., Newton iteration, Gauss eliminations and Gram-Schmidt orthogonalization.) That hints that you might be using symbolic methods-or perhaps a hybrid numeric-symbolic method?īy using the specifics of the system of linear equations (very sparse matrix), we subdivide the set of all equations into small groups and solve these small subsystems corresponding to these groups. Now we can try to go away from the feature based approach with its notorious history tree and to unify in one 3D workspace parametric and direct modeling approaches. That’s why complicated solid model is divided into hierarchic list of simple features (each one having its own parametric sketch) – known as “history tree”.īut we have a solver that is powerful enough to constrain the whole 3D model (using all reasonable 3D constraints). The reason for this is quite simple – these solvers can resolve only small models. Traditional parametric CAD lives only in 2D sections – this is part of “parametric feature-based approach” to solid modeling. Actually, this is the most interesting direction.
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I do apologize that I can’t provide you the detailed information about our algorithm (there is a remarkable mathematic work behind this and five or six PhD dissertations in some of the leading USA universities – in the end of the nineties this issue was in focus of the researchers), but I want to mention one additional advantage of the approach – our methods are well suited for parallel processing.Ī: So far we tested our solver in 2D sketcher only, but I don’t see any reasons why it shouldn’t work for 3D constraints as well. That is exactly what we managed to do in our Cheetah solver. If you can use this information efficiently, you will dramatically improve performance and decrease memory requirements of the solver. We know in advance that each row of this matrix has a fixed number of non-zeros (let’s say, not more than twenty non-zeros). But the system of linear equations that appears in CAD is not “general purpose” – the matrix of such a system is very sparse. Modern solvers (that of PTC) use general purpose methods of linear algebra. The situation is similar with other solvers). Q: What are you doing differently in Cheetah that what’s being done with other 2D constraint solvers?Ī: The main advantage of our solver is that it has O(n) memory and time requirements (to compare, solver of PTC requires O(n 2) amount of memory and O(n 3) arithmetic operations to solve a system of constraint equations. Lev Kantorovich, from Cloud Invent, responded to my questions. I also duplicated the demo from the videos using Autodesk Inventor, which uses Siemens PLM’s 2D DCM constraint manager. I chatted (by email) last week with both the folks from Cloud Invent, and from PTC, to try and understand what I was really seeing. First, the Creo Parametric solver seems to fall apart (become unstable) once faced with a large sketch. If you take the time to watch these two videos, you’ll see a couple of important things. The next video they posted was of their “Cheetah” solver, running on an identical sketch.
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The first video showed the performance of the sketcher in PTC Creo Parametric 1.0, when dealing with massively large sketches.
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They’re pretty important, and have a significant effect on a CAD program’s performance.Ĭloud Invent, a small software developer, made up-so far as I can tell-mostly of PhD mathematicians, recently posted a couple of interesting videos on YouTube. They’re also used behind the scenes in direct modeling CAD systems. Solvers are one of the major components used in 3D CAD programs, and are the main part of the sketcher used in parametric feature (history based) modelers. Last week, I wrote, in Solving the CAD concurrency problem, about 2D geometric constraint solvers.