Comments on: Triangles, interpolation and the math I forgot http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/ About Flash, kites and other happy things Sun, 30 May 2010 08:16:10 +0000 http://wordpress.org/?v=2.9.2 hourly 1 By: epologee http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-97 epologee Thu, 04 Feb 2010 16:10:33 +0000 http://epologee.com/blog/?p=134#comment-97 That sounds like a valuable addition, mdmx! I tried out code to find the enclosing triangle, but still found that there were area's that would 'break' the smooth transitions. Would like to see your solution! That sounds like a valuable addition, mdmx! I tried out code to find the enclosing triangle, but still found that there were area’s that would ‘break’ the smooth transitions. Would like to see your solution!

]]> By: mdmx http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-96 mdmx Thu, 04 Feb 2010 14:40:56 +0000 http://epologee.com/blog/?p=134#comment-96 I'm working with quite similar project. I am creating depth map from control point soap. Points are not in order, they have x,y and depth, and i need to create nice and smooth map out of them. Instead of getting three of the closest point, i am finding the closest points which products a tringle which encloses the point of interest. That's not the same than using just three closest point. It removes most of the errors that can be seen in your picture. If i can't find the enclosing triangle, the point is stated as 'unknown'. But in your case, if you want to calculate areas outside the 'polygon', you can simply use the two of the closest point and interpolate between them. As there is no enclosing triangle, there is no need to use three values in interpolating, two is enough. You gain nothing by using three. I can post the code which finds the triangle, if you want it. I’m working with quite similar project. I am creating depth map from control point soap. Points are not in order, they have x,y and depth, and i need to create nice and smooth map out of them.

Instead of getting three of the closest point, i am finding the closest points which products a tringle which encloses the point of interest. That’s not the same than using just three closest point.

It removes most of the errors that can be seen in your picture.

If i can’t find the enclosing triangle, the point is stated as ‘unknown’. But in your case, if you want to calculate areas outside the ‘polygon’, you can simply use the two of the closest point and interpolate between them. As there is no enclosing triangle, there is no need to use three values in interpolating, two is enough. You gain nothing by using three.

I can post the code which finds the triangle, if you want it.

]]> By: epologee http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-68 epologee Sat, 14 Nov 2009 09:53:05 +0000 http://epologee.com/blog/?p=134#comment-68 Awesome comment, thanks Huffman! I'll be sure to try it out on the weighted triangles. I still need the above method for points outside of the triangles though, since it's easy to get outside of the mesh if you're on a map with limited data points. Awesome comment, thanks Huffman! I’ll be sure to try it out on the weighted triangles. I still need the above method for points outside of the triangles though, since it’s easy to get outside of the mesh if you’re on a map with limited data points.

]]> By: Huffman http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-67 Huffman Sat, 14 Nov 2009 07:38:02 +0000 http://epologee.com/blog/?p=134#comment-67 Oh I forgot to paste the link that has the (very easy) calculations: http://www.ems-i.com/smshelp/Data_Module/Interpolation/Linear_Interpolationsms.htm The "elevation" z, which is mentioned, is is the grayscale color component. Make a new plane for each color. Oh I forgot to paste the link that has the (very easy) calculations: http://www.ems-i.com/smshelp/Data_Module/Interpolation/Linear_Interpolationsms.htm

The “elevation” z, which is mentioned, is is the grayscale color component. Make a new plane for each color.

]]> By: Huffman http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-66 Huffman Sat, 14 Nov 2009 07:35:05 +0000 http://epologee.com/blog/?p=134#comment-66 Hi, cool shading method! I should however add that this is not an exactly linear inerpolation as was probably your intent. I implemented a similar problem with a 3D plane: With the 3 triangle points, you can simply a mathematical function z(x,y). x,y are your pixels and z is the color. You calculate 3 planes (one for each color), which gives you a 100% exact linear interpolation. Also this might probably be even faster, as I think your distance calculation involves several square roots? Anyway, you definitely came up with a cool method. But if you need an accurate linear interpolation in the future, this is the math you forgot ;) Hi, cool shading method! I should however add that this is not an exactly linear inerpolation as was probably your intent. I implemented a similar problem with a 3D plane:
With the 3 triangle points, you can simply a mathematical function z(x,y). x,y are your pixels and z is the color.

You calculate 3 planes (one for each color), which gives you a 100% exact linear interpolation.
Also this might probably be even faster, as I think your distance calculation involves several square roots?

Anyway, you definitely came up with a cool method. But if you need an accurate linear interpolation in the future, this is the math you forgot ;)

]]> By: epologee.com blog » Blog Archive » Nuon Solar Race Holland http://epologee.com/blog/2009/triangles-interpolation-and-the-math-i-forgot/comment-page-1/#comment-52 epologee.com blog » Blog Archive » Nuon Solar Race Holland Fri, 18 Sep 2009 13:30:39 +0000 http://epologee.com/blog/?p=134#comment-52 [...] project, and had great fun laying out the technical details, from little race car animations to weather data interpolation. Thank you, Media Republic, for having this [...] [...] project, and had great fun laying out the technical details, from little race car animations to weather data interpolation. Thank you, Media Republic, for having this [...]

]]>