Hi
Im trying to create a virtual Harmonograph based upon Wiki page Harmonograph - Wikipedia, the free encyclopedia
The spreadsheet (can be downloaded at http://spotprints.co.uk/harmonograph.xlsx) does go some way to that but I want to use the x,y values in Coreldraw and want to keep the number of points to plot to a minimum and yet have a smooth curve that accurately reflects a real harmonograph.
If I use a regular period of time between steps I come accross one of two problems - either;
a long period between steps works for most of the drawing but produces inaccurate curves when it is asked to draw between two points at acute angles, or
a short period between steps draws even the acute angles accurately but produces so many points (most of them on fairly flat curves) that it makes working with the curves difficult because what I would like to be one curve has to be broken up into several pieces in order for Coreldraw to use them.
I have not been able to solve the mathematical problem of when more points would be useful but think it relates to the tangents of each point compared to the points before/after and wonder if someone might help with that. From reading around this site, I think if the - when to draw extra points problem - can be solved the next stage would be to add lines in the spreadsheet so that the steps at points where the curve is acute are smaller than where it is relatively flat.
Any help would be appreciated.
nicksoph
Im trying to create a virtual Harmonograph based upon Wiki page Harmonograph - Wikipedia, the free encyclopedia
The spreadsheet (can be downloaded at http://spotprints.co.uk/harmonograph.xlsx) does go some way to that but I want to use the x,y values in Coreldraw and want to keep the number of points to plot to a minimum and yet have a smooth curve that accurately reflects a real harmonograph.
If I use a regular period of time between steps I come accross one of two problems - either;
a long period between steps works for most of the drawing but produces inaccurate curves when it is asked to draw between two points at acute angles, or
a short period between steps draws even the acute angles accurately but produces so many points (most of them on fairly flat curves) that it makes working with the curves difficult because what I would like to be one curve has to be broken up into several pieces in order for Coreldraw to use them.
I have not been able to solve the mathematical problem of when more points would be useful but think it relates to the tangents of each point compared to the points before/after and wonder if someone might help with that. From reading around this site, I think if the - when to draw extra points problem - can be solved the next stage would be to add lines in the spreadsheet so that the steps at points where the curve is acute are smaller than where it is relatively flat.
Any help would be appreciated.
nicksoph
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