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< div id = "projectbrief" > Set of algorithms implemented in C.< / div >
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< a href = "#define-members" > Macros< / a > |
< a href = "#func-members" > Functions< / a > < / div >
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< div class = "title" > spirograph.c File Reference< / div > < / div >
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< p > Implementation of < a href = "https://en.wikipedia.org/wiki/Spirograph" > Spirograph< / a >
< a href = "#details" > More...< / a > < / p >
< div class = "textblock" > < code > #include < math.h> < / code > < br / >
< code > #include < stdbool.h> < / code > < br / >
< code > #include < stdio.h> < / code > < br / >
< code > #include < stdlib.h> < / code > < br / >
< code > #include < time.h> < / code > < br / >
< / div > < div class = "textblock" > < div class = "dynheader" >
Include dependency graph for spirograph.c:< / div >
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< div class = "center" > < iframe scrolling = "no" frameborder = "0" src = "../../da/dd5/spirograph_8c__incl.svg" width = "430" height = "112" > < p > < b > This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.< / b > < / p > < / iframe >
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< tr class = "heading" > < td colspan = "2" > < h2 class = "groupheader" > < a name = "define-members" > < / a >
Macros< / h2 > < / td > < / tr >
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#define  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d7/d98/spirograph_8c.html#a525335710b53cb064ca56b936120431e" > _USE_MATH_DEFINES< / a > < / td > < / tr >
< tr class = "memdesc:a525335710b53cb064ca56b936120431e" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > required for MSVC compiler < br / > < / td > < / tr >
< tr class = "separator:a525335710b53cb064ca56b936120431e" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "heading" > < td colspan = "2" > < h2 class = "groupheader" > < a name = "func-members" > < / a >
Functions< / h2 > < / td > < / tr >
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< tr class = "memitem:a0daa148091ec953809fc172289f773d3" > < td class = "memItemLeft" align = "right" valign = "top" > void  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d7/d98/spirograph_8c.html#a0daa148091ec953809fc172289f773d3" > spirograph< / a > (double *x, double *y, double l, double k, size_t N, double rot)< / td > < / tr >
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< tr class = "memdesc:a0daa148091ec953809fc172289f773d3" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Generate spirograph curve into arrays < code > x< / code > and < code > y< / code > such that the i^th point in 2D is represented by < code > (x[i],y[i])< / code > . < a href = "../../d7/d98/spirograph_8c.html#a0daa148091ec953809fc172289f773d3" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:a0daa148091ec953809fc172289f773d3" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:a708a4c1a4d0c4acc4c447310dd4db27f" > < td class = "memItemLeft" align = "right" valign = "top" > < a id = "a708a4c1a4d0c4acc4c447310dd4db27f" > < / a >
void  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d7/d98/spirograph_8c.html#a708a4c1a4d0c4acc4c447310dd4db27f" > test< / a > (void)< / td > < / tr >
< tr class = "memdesc:a708a4c1a4d0c4acc4c447310dd4db27f" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Test function to save resulting points to a CSV file. < br / > < / td > < / tr >
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int  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../d7/d98/spirograph_8c.html#a3c04138a5bfe5d72780bb7e82a18e627" > main< / a > (int argc, char **argv)< / td > < / tr >
< tr class = "memdesc:a3c04138a5bfe5d72780bb7e82a18e627" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Main function. < br / > < / td > < / tr >
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< / table >
< a name = "details" id = "details" > < / a > < h2 class = "groupheader" > Detailed Description< / h2 >
< div class = "textblock" > < p > Implementation of < a href = "https://en.wikipedia.org/wiki/Spirograph" > Spirograph< / a > < / p >
< dl class = "section author" > < dt > Author< / dt > < dd > < a href = "https://github.com/kvedala" > Krishna Vedala< / a > < / dd > < / dl >
< p > Implementation of the program is based on the geometry shown in the figure below:< / p >
< p > < a href = "https://commons.wikimedia.org/wiki/File:Resonance_Cascade.svg" > < img src = "https://upload.wikimedia.org/wikipedia/commons/3/39/Resonance_Cascade.svg" alt = "Spirograph geometry from Wikipedia" style = "pointer-events: none; width: 250px" class = "inline" / > < / a > < / p >
< / div > < h2 class = "groupheader" > Function Documentation< / h2 >
< a id = "a0daa148091ec953809fc172289f773d3" > < / a >
< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a0daa148091ec953809fc172289f773d3" > ◆ < / a > < / span > spirograph()< / h2 >
< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > void spirograph < / td >
< td > (< / td >
< td class = "paramtype" > double *  < / td >
< td class = "paramname" > < em > x< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > double *  < / td >
< td class = "paramname" > < em > y< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > double  < / td >
< td class = "paramname" > < em > l< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > double  < / td >
< td class = "paramname" > < em > k< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > size_t  < / td >
< td class = "paramname" > < em > N< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > double  < / td >
< td class = "paramname" > < em > rot< / em >   < / td >
< / tr >
< tr >
< td > < / td >
< td > )< / td >
< td > < / td > < td > < / td >
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< / div > < div class = "memdoc" >
< p > Generate spirograph curve into arrays < code > x< / code > and < code > y< / code > such that the i^th point in 2D is represented by < code > (x[i],y[i])< / code > . < / p >
< p > The generating function is given by: < / p > < p class = "formulaDsp" >
\begin{eqnarray*} x & =& R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right) \right]\\ y & =& R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right) \right] \end{eqnarray*}
< / p >
< p > where< / p > < ul >
< li > \(R\) is the scaling parameter that we will consider \(=1\)< / li >
< li > \(l=\frac{\rho}{r}\) is the relative distance of marker from the centre of inner circle and \(0\le l\le1\)< / li >
< li > \(\rho\) is physical distance of marker from centre of inner circle< / li >
< li > \(r\) is the radius of inner circle< / li >
< li > \(k=\frac{r}{R}\) is the ratio of radius of inner circle to outer circle and \(0< k< 1\)< / li >
< li > \(R\) is the radius of outer circle< / li >
< li > \(t\) is the angle of rotation of the point i.e., represents the time parameter< / li >
< / ul >
< p > Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.< / p >
< dl class = "params" > < dt > Parameters< / dt > < dd >
< table class = "params" >
< tr > < td class = "paramdir" > [out]< / td > < td class = "paramname" > x< / td > < td > output array containing absicca of points (must be pre-allocated) < / td > < / tr >
< tr > < td class = "paramdir" > [out]< / td > < td class = "paramname" > y< / td > < td > output array containing ordinates of points (must be pre-allocated) < / td > < / tr >
< tr > < td class = "paramdir" > < / td > < td class = "paramname" > l< / td > < td > the relative distance of marker from the centre of inner circle and \(0\le l\le1\) < / td > < / tr >
< tr > < td class = "paramdir" > < / td > < td class = "paramname" > k< / td > < td > the ratio of radius of inner circle to outer circle and \(0< k< 1\) < / td > < / tr >
< tr > < td class = "paramdir" > < / td > < td class = "paramname" > N< / td > < td > number of sample points along the trajectory (higher = better resolution but consumes more time and memory) < / td > < / tr >
< tr > < td class = "paramdir" > < / td > < td class = "paramname" > num_rot< / td > < td > the number of rotations to perform (can be fractional value) < / td > < / tr >
< / table >
< / dd >
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< div class = "fragment" > < div class = "line" > < a name = "l00058" > < / a > < span class = "lineno" > 58< / span >   {< / div >
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< div class = "line" > < a name = "l00059" > < / a > < span class = "lineno" > 59< / span >   < span class = "keywordtype" > double< / span > dt = rot * 2.f * M_PI / N;< / div >
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< div class = "line" > < a name = "l00060" > < / a > < span class = "lineno" > 60< / span >   < span class = "keywordtype" > double< / span > t = 0.f, R = 1.f;< / div >
< div class = "line" > < a name = "l00061" > < / a > < span class = "lineno" > 61< / span >   < span class = "keyword" > const< / span > < span class = "keywordtype" > double< / span > k1 = 1.f - k;< / div >
< div class = "line" > < a name = "l00062" > < / a > < span class = "lineno" > 62< / span >   < / div >
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< div class = "line" > < a name = "l00063" > < / a > < span class = "lineno" > 63< / span >   < span class = "keywordflow" > for< / span > (< span class = "keywordtype" > size_t< / span > dk = 0; dk < N; dk++, t += dt)< / div >
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< div class = "line" > < a name = "l00064" > < / a > < span class = "lineno" > 64< / span >   {< / div >
< div class = "line" > < a name = "l00065" > < / a > < span class = "lineno" > 65< / span >   x[dk] = R * (k1 * cos(t) + l * k * cos(k1 * t / k));< / div >
< div class = "line" > < a name = "l00066" > < / a > < span class = "lineno" > 66< / span >   y[dk] = R * (k1 * sin(t) - l * k * sin(k1 * t / k));< / div >
< div class = "line" > < a name = "l00067" > < / a > < span class = "lineno" > 67< / span >   }< / div >
< div class = "line" > < a name = "l00068" > < / a > < span class = "lineno" > 68< / span >   }< / div >
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