3 ms·

Did the course have a text book? If so, which one/ones?

globuous 9y ago
I didn't have a textbook for mine, just class notes. But I remember there was some topology, required for defining manifolds and their relations with one another so that it makes "sense". here's a book that your might find interesting: https://www.amazon.com/Geometry-Computer-Graphics-Undergraduate-Mathematics/dp/1852338016 https://www.amazon.com/Geometry-Computer-Graphics-Undergradu... On a side not, a lot of current research focuses on simplifying CAD models to use them as inputs to simulation programs (CFD, finite element analysis codes etc). Indeed, since your CAD model is highly precise, the models are hard to mesh (need very fine mesh to discretize the details), so you simplify them manually and it's very time consuming. One of the methods that most struck me to automate this simplification was taking the CAD model, transforming it to the frequency domain where high frequencies represent small geometric details and large frequencies, larges underlying features in the model's geometry. So you can filter out the high frequencies, transform it back and end up with a simplified model. You've literally filtered away the smaller geometric features of the model. I remember the paper describing the method for 2D geometry only. Here's a paper surveying the some of the state of the art methods to simplify CAD models and prepare them for simulation packages. https://www.sciencedirect.com/science/article/pii/S0010448508002285 https://www.sciencedirect.com/science/article/pii/S001044850...
- bringtheaction 9y ago
  > One of the methods that most struck me to automate this simplification was taking the CAD model, transforming it to the frequency domain where high frequencies represent small geometric details and large frequencies, larges underlying features in the model's geometry. So you can filter out the high frequencies, transform it back and end up with a simplified model. You've literally filtered away the smaller geometric features of the model. That’s a very interesting idea. I guess the problem is though, how would you be able to make such a transformation?
jacobolus 9y ago
I recommend the book Curves and Surfaces for CAGD by Gerald Farin (RIP). I have the 4th edition, which I have seen some people recommend in preference to the 5th, but I have never looked at the 5th edition.

I didn't have a textbook for mine, just class notes. But I remember there was some topology, required for defining manifolds and their relations with one another so that it makes "sense". here's a book that your might find interesting: https://www.amazon.com/Geometry-Computer-Graphics-Undergraduate-Mathematics/dp/1852338016 https://www.amazon.com/Geometry-Computer-Graphics-Undergradu... On a side not, a lot of current research focuses on simplifying CAD models to use them as inputs to simulation programs (CFD, finite element analysis codes etc). Indeed, since your CAD model is highly precise, the models are hard to mesh (need very fine mesh to discretize the details), so you simplify them manually and it's very time consuming. One of the methods that most struck me to automate this simplification was taking the CAD model, transforming it to the frequency domain where high frequencies represent small geometric details and large frequencies, larges underlying features in the model's geometry. So you can filter out the high frequencies, transform it back and end up with a simplified model. You've literally filtered away the smaller geometric features of the model. I remember the paper describing the method for 2D geometry only. Here's a paper surveying the some of the state of the art methods to simplify CAD models and prepare them for simulation packages. https://www.sciencedirect.com/science/article/pii/S0010448508002285 https://www.sciencedirect.com/science/article/pii/S001044850...

bringtheaction 9y ago
> One of the methods that most struck me to automate this simplification was taking the CAD model, transforming it to the frequency domain where high frequencies represent small geometric details and large frequencies, larges underlying features in the model's geometry. So you can filter out the high frequencies, transform it back and end up with a simplified model. You've literally filtered away the smaller geometric features of the model. That’s a very interesting idea. I guess the problem is though, how would you be able to make such a transformation?

jacobolus 9y ago

I recommend the book Curves and Surfaces for CAGD by Gerald Farin (RIP). I have the 4th edition, which I have seen some people recommend in preference to the 5th, but I have never looked at the 5th edition.