RE: Hi I'm new
Cartesian equation: x2 + y2 = a2 or parametrically: x = a cos(t), y = a sin(t) Polar equation: r = a but the rest is at... http://www.ussc.alltheweb.com/cgi-bin/search?exec=FAST+Search&type=all&query =code+pixels+circle+points even if you can't plot using the pencil tool, you can estimate the sizes using the circle as a rectangle... scripting left as an excercise! Xavier > > > I've been reading the list heaps and finding out almost all > > that I need to > > > know at this stage but I have one big problem. > > > > > > I am developing a stack that needs to redraw an ellipse and a > > circular arc > > > that intersects with the ellipse at two points. I thought > that the oval > > > graphic was the best tool for the job but how do I find the > > intersection > > > points. The rect of the arc is set and the user sets the rect of the > > > ellipse. I really only need to know the x coordinates so I can > > calculate the > > > arcAngle and the startAngle of the arc. > > > > > > My understanding is that an oval has no real mathematical > > definition so is > > > the oval tool actually an ellipse? > > a little meta geometry should help here... > given that im not sure what you mean with elipses and ovals (pretty > ambiguous here) > you can do a lot of precise enough calculations with geometry... > If you draw a rectangle (rect) over that same oval you have an easier view > to "estimate" your points... > > the thing is algebra level, and it's easy to find code (borrowed from c or > java anywhere on the net... (all the keywords for the search are in that > previous sentence - will take ya right to it). There's also tons of good > programming books on this subject! im a little tempted to do some too > lately... i'll c what I can find! > > http://www.mathcom.com/nafaq/q230.8.html > http://www.mathcom.com/nafaq/q285.html > and > http://www.primenet.com/~grieggs/cg_faq.html > > draw a circle as a Bezier (or B-spline) curve? > http://www.primenet.com/~grieggs/cg_faq.html#Howto_Spline > tell whether a point is within a planar polygon? > http://www.primenet.com/~grieggs/cg_faq.html#Howto_PIP > > in sum without code or more > there I found... > > How do I draw a circle as a Bezier (or B-spline) curve? > The short answer is, "You can't." Unless you use a rational spline you can > only approximate a circle. The approximation may look acceptable, > but it is > sensitive to scale. Magnify the scale and the error of approximation > magnifies. Deviations from circularity that were not visible in the small > can become glaring in the large. If you want to do the job right, consult > the article: > "A Menagerie of Rational B-Spline Circles" by Leslie Piegl and > Wayne Tiller > in IEEE Computer Graphics and Applications, volume 9, number 9, September, > 1989, pages 48-56. > (www.ieee.org or something like that...) > > For rough, non-rational approximations, consult the book: > > Computational Geometry for Design and Manufacture by I. D. Faux and M. J. > Pratt, Ellis Horwood Publishers, Halsted Press, John Wiley 1980. > > For the best known non-rational approximations, consult the article: > > "Good Approximation of Circles by Curvature-continuous Bezier > Curves" by Tor > Dokken, Morten Daehlen, Tom Lyche, and Knut Morken in Computer Aided > Geometric Design, volume 7, numbers 1-4 (combined), June, 1990, > pages 33-41 > [Elsevier Science Publishers (North-Holland)] > > > How do I tell whether a point is within a planar polygon? > Consider a ray originating at the point of interest and continuing to > infinity. If it crosses an odd number of polygon edges along the way, the > point is within the polygon. If the ray crosses an even number of > edges, the > point is either outside the polygon, or within an interior hole > formed from > intersecting polygon edges. This idea is known in the trade as the Jordan > curve theorem; see Eric Haines' article in Glassner's ray tracing book > (above) for more information, including treatment of special cases. > Another method is to sum the absolute angles from the point to all the > vertices on the polygon. If the sum is 2 pi, the point is inside, > if the sum > is 0 the point is outside. However, this method is about an order of > magnitude slower than the previous method because evaluating the > trigonometric functions is usually quite costly. > > www.ddj.com might have some nice algorythms too!!! almost forgot my bible! > > > Archives: http://www.mail-archive.com/metacard%40lists.best.com/ > Info: http://www.xworlds.com/metacard/mailinglist.htm > Please send bug reports to <[EMAIL PROTECTED]>, not this list. > Archives: http://www.mail-archive.com/metacard%40lists.best.com/ Info: http://www.xworlds.com/metacard/mailinglist.htm Please send bug reports to <[EMAIL PROTECTED]>, not this list.
RE: Hi I'm new
> > I've been reading the list heaps and finding out almost all > that I need to > > know at this stage but I have one big problem. > > > > I am developing a stack that needs to redraw an ellipse and a > circular arc > > that intersects with the ellipse at two points. I thought that the oval > > graphic was the best tool for the job but how do I find the > intersection > > points. The rect of the arc is set and the user sets the rect of the > > ellipse. I really only need to know the x coordinates so I can > calculate the > > arcAngle and the startAngle of the arc. > > > > My understanding is that an oval has no real mathematical > definition so is > > the oval tool actually an ellipse? a little meta geometry should help here... given that im not sure what you mean with elipses and ovals (pretty ambiguous here) you can do a lot of precise enough calculations with geometry... If you draw a rectangle (rect) over that same oval you have an easier view to "estimate" your points... the thing is algebra level, and it's easy to find code (borrowed from c or java anywhere on the net... (all the keywords for the search are in that previous sentence - will take ya right to it). There's also tons of good programming books on this subject! im a little tempted to do some too lately... i'll c what I can find! http://www.mathcom.com/nafaq/q230.8.html http://www.mathcom.com/nafaq/q285.html and http://www.primenet.com/~grieggs/cg_faq.html draw a circle as a Bezier (or B-spline) curve? http://www.primenet.com/~grieggs/cg_faq.html#Howto_Spline tell whether a point is within a planar polygon? http://www.primenet.com/~grieggs/cg_faq.html#Howto_PIP in sum without code or more there I found... How do I draw a circle as a Bezier (or B-spline) curve? The short answer is, "You can't." Unless you use a rational spline you can only approximate a circle. The approximation may look acceptable, but it is sensitive to scale. Magnify the scale and the error of approximation magnifies. Deviations from circularity that were not visible in the small can become glaring in the large. If you want to do the job right, consult the article: "A Menagerie of Rational B-Spline Circles" by Leslie Piegl and Wayne Tiller in IEEE Computer Graphics and Applications, volume 9, number 9, September, 1989, pages 48-56. (www.ieee.org or something like that...) For rough, non-rational approximations, consult the book: Computational Geometry for Design and Manufacture by I. D. Faux and M. J. Pratt, Ellis Horwood Publishers, Halsted Press, John Wiley 1980. For the best known non-rational approximations, consult the article: "Good Approximation of Circles by Curvature-continuous Bezier Curves" by Tor Dokken, Morten Daehlen, Tom Lyche, and Knut Morken in Computer Aided Geometric Design, volume 7, numbers 1-4 (combined), June, 1990, pages 33-41 [Elsevier Science Publishers (North-Holland)] How do I tell whether a point is within a planar polygon? Consider a ray originating at the point of interest and continuing to infinity. If it crosses an odd number of polygon edges along the way, the point is within the polygon. If the ray crosses an even number of edges, the point is either outside the polygon, or within an interior hole formed from intersecting polygon edges. This idea is known in the trade as the Jordan curve theorem; see Eric Haines' article in Glassner's ray tracing book (above) for more information, including treatment of special cases. Another method is to sum the absolute angles from the point to all the vertices on the polygon. If the sum is 2 pi, the point is inside, if the sum is 0 the point is outside. However, this method is about an order of magnitude slower than the previous method because evaluating the trigonometric functions is usually quite costly. www.ddj.com might have some nice algorythms too!!! almost forgot my bible! Archives: http://www.mail-archive.com/metacard%40lists.best.com/ Info: http://www.xworlds.com/metacard/mailinglist.htm Please send bug reports to <[EMAIL PROTECTED]>, not this list.
RE: Hi I'm new
On Thu, 21 Sep 2000, Monte Goulding wrote: > I've been reading the list heaps and finding out almost all that I need to > know at this stage but I have one big problem. > > I am developing a stack that needs to redraw an ellipse and a circular arc > that intersects with the ellipse at two points. I thought that the oval > graphic was the best tool for the job but how do I find the intersection > points. The rect of the arc is set and the user sets the rect of the > ellipse. I really only need to know the x coordinates so I can calculate the > arcAngle and the startAngle of the arc. > > My understanding is that an oval has no real mathematical definition so is > the oval tool actually an ellipse? Yes: Blame the HyperCard developers for this abuse of mathematical terminology, which we just followed. > If so can I obtain the submajor and > subminor axes of that ellipse? Given the imprecision associated with drawing ellipses and the differences in how they're drawn on the different platforms (and believe me, we've tried long and hard to eliminate or at least minimize these) IMHO you're probably not going to be able to do what you want using this style of graphic. Instead, I recommend using a polygon object and generating the points of the arcs and ellipses (and whatever other shapes you need) with scripts. This way you can be exactly sure where the points are, and that you have enough of them to make a smooth shape at any size. It does require a little math (high-school geometry), but doing it this way will save you a lot of time and headache in the long run. > My other big question was why when we build a standalone there is no > facility to set icons for that standalone other than 0(standalone builder > custom prop mcappicon). I am planning to modify the standalone builder so > that i can set an icon for a custom file type as icon 1(standalone builder > custom prop mcdocicon). Is this modification a breach of license or > anything? It would be really good If in future versions of MetaCard the > engine had a couple more dummy icons in icon 2 & 3 so we could play with > these too. There are two icons in the Win32 engine, one for the app and one for a document icon. You can change the first using the standalone builder, but you'd have to change the second with an icon editor (like AX-Icons) that can edit icons in place. I'll submit a feature-request for a way to change the second one in the standalone builder too. Regards, Scott > Regards > Monte Goulding Scott Raney [EMAIL PROTECTED] http://www.metacard.com MetaCard: You know, there's an easier way to do that... Archives: http://www.mail-archive.com/metacard%40lists.best.com/ Info: http://www.xworlds.com/metacard/mailinglist.htm Please send bug reports to <[EMAIL PROTECTED]>, not this list.
RE: Hi I'm new
Hi List I've been reading the list heaps and finding out almost all that I need to know at this stage but I have one big problem. I am developing a stack that needs to redraw an ellipse and a circular arc that intersects with the ellipse at two points. I thought that the oval graphic was the best tool for the job but how do I find the intersection points. The rect of the arc is set and the user sets the rect of the ellipse. I really only need to know the x coordinates so I can calculate the arcAngle and the startAngle of the arc. My understanding is that an oval has no real mathematical definition so is the oval tool actually an ellipse? If so can I obtain the submajor and subminor axes of that ellipse? My other big question was why when we build a standalone there is no facility to set icons for that standalone other than 0(standalone builder custom prop mcappicon). I am planning to modify the standalone builder so that i can set an icon for a custom file type as icon 1(standalone builder custom prop mcdocicon). Is this modification a breach of license or anything? It would be really good If in future versions of MetaCard the engine had a couple more dummy icons in icon 2 & 3 so we could play with these too. Regards Monte Goulding _ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Share information about yourself, create your own public profile at http://profiles.msn.com. Archives: http://www.mail-archive.com/metacard%40lists.best.com/ Info: http://www.xworlds.com/metacard/mailinglist.htm Please send bug reports to <[EMAIL PROTECTED]>, not this list.
