Perl ABCMath::Bezier - Find the coordinates of a Bezier curve with Perl
Use the Math::Bezier module to find the coordinates of a Bezier curve in Perl. You can specify a control point and get the coordinates of the curve along it by dividing it.
use Math::Bezier; # (x, y) Create a curve by passing a list of control points my $bezier = Math::Bezier->new($x1, $y1, $x2, $y2, ..., $xn, $yn); # Pass the reference instead my $bezier = Math::Bezier->new([$x1, $y1, $x2, $y2, ..., $xn, $yn]); # Determine the point(x, y) in the curve. Specify a range from 0 to 1. my ($x, $y) = $bezier->point(0.5); # Returns a list in scalar context my $xy = $bezier->point(0.5); # Returns the (x, y) points divided into 20 along the curve. my @curve = $bezier->curve(20); # Receive in reference my $curve = $bezier->curve(20);
A example that draws a 3D Bezier curve and divides it into 100 points
Bezier curves are often used in 3D, so here is an example of drawing a 3D Bezier curve and dividing it into 100 points.
The control points are (0, 0), (10, 10), (20, 40). For a 3D Bezier curve, specify three points as control points.
The straight line connecting the first control point and the second control point is the tangent to the curve at the first control point.
The straight line connecting the second control point and the third control point is the tangent to the curve at the third control point.
use strict;
use warnings;
use Math::Bezier;
# List of control points (x, y)
my $bezier = Math::Bezier->new(0, 0, 10, 10, 20, 40);
my $curve_points = $bezier->curve(100);
for (my $i = 0; $i < @$curve_points; $i += 2) {
my $x = $curve_points->[$i];
my $y = $curve_points->[$i + 1];
print "($x, $y)\n";
}
The output will show 100 points along the 3D Bezier curve.
(0, 0) (0.202020202020202, 0.204060810121416) (0.404040404040404, 0.412202836445261) (0.606060606060606, 0.624426078971533) (0.808080808080808, 0.840730537700235) (1.01010101010101, 1.06111621263136) (1.21212121212121, 1.28558310376492) (1.41414141414141, 1.51413121110091) (1.61616161616162, 1.74676053463932) (1.81818181818182, 1.98347107438017) (2.02020202020202, 2.22426283032344) (2.22222222222222, 2.46913580246914) (2.42424242424242, 2.71808999081726) (2.62626262626263, 2.97112539536782) (2.82828282828283, 3.2282420161208) (3.03030303030303, 3.48943985307622) (3.23232323232323, 3.75471890623406) (3.43434343434343, 4.02407917559433) (3.63636363636364, 4.29752066115702) (3.83838383838384, 4.57504336292215) (4.04040404040404, 4.8566472808897) (4.24242424242424, 5.14233241505969) (4.44444444444444, 5.4320987654321) (4.64646464646465, 5.72594633200694) (4.84848484848485, 6.02387511478421) (5.05050505050505, 6.3258851137639) (5.25252525252525, 6.63197632894603) (5.45454545454545, 6.94214876033058) (5.65656565656566, 7.25640240791756) (5.85858585858586, 7.57473727170697) (6.06060606060606, 7.89715335169881) (6.26262626262626, 8.22365064789307) (6.46464646464647, 8.55422916028977) (6.66666666666667, 8.88888888888889) (6.86868686868687, 9.22762983369044) (7.07070707070707, 9.57045199469442) (7.27272727272727, 9.91735537190083) (7.47474747474747, 10.2683399653097) (7.67676767676768, 10.6234057749209) (7.87878787878788, 10.9825528007346) (8.08080808080808, 11.3457810427507) (8.28282828282828, 11.7130905009693) (8.48484848484848, 12.0844811753903) (8.68686868686869, 12.4599530660137) (8.88888888888889, 12.8395061728395) (9.09090909090909, 13.2231404958678) (9.29292929292929, 13.6108560350985) (9.49494949494949, 14.0026527905316) (9.6969696969697, 14.3985307621671) (9.8989898989899, 14.7984899500051) (10.1010101010101, 15.2025303540455) (10.3030303030303, 15.6106519742883) (10.5050505050505, 16.0228548107336) (10.7070707070707, 16.4391388633813) (10.9090909090909, 16.8595041322314) (11.1111111111111, 17.283950617284) (11.3131313131313, 17.7124783185389) (11.5151515151515, 18.1450872359963) (11.7171717171717, 18.5817773696562) (11.9191919191919, 19.0225487195184) (12.1212121212121, 19.4674012855831) (12.3232323232323, 19.9163350678502) (12.5252525252525, 20.3693500663198) (12.7272727272727, 20.8264462809917) (12.9292929292929, 21.2876237118661) (13.1313131313131, 21.752882358943) (13.3333333333333, 22.2222222222222) (13.5353535353535, 22.6956433017039) (13.7373737373737, 23.173145597388) (13.9393939393939, 23.6547291092746) (14.1414141414141, 24.1403938373635) (14.3434343434343, 24.6301397816549) (14.5454545454545, 25.1239669421488) (14.7474747474747, 25.621875318845) (14.9494949494949, 26.1238649117437) (15.1515151515152, 26.6299357208448) (15.3535353535354, 27.1400877461483) (15.5555555555556, 27.6543209876543) (15.7575757575758, 28.1726354453627) (15.959595959596, 28.6950311192735) (16.1616161616162, 29.2215080093868) (16.3636363636364, 29.7520661157025) (16.5656565656566, 30.2867054382206) (16.7676767676768, 30.8254259769411) (16.969696969697, 31.3682277318641) (17.1717171717172, 31.9151107029895) (17.3737373737374, 32.4660748903173) (17.5757575757576, 33.0211202938476) (17.7777777777778, 33.5802469135802) (17.979797979798, 34.1434547495154) (18.1818181818182, 34.7107438016529) (18.3838383838384, 35.2821140699929) (18.5858585858586, 35.8575655545352) (18.7878787878788, 36.4370982552801) (18.989898989899, 37.0207121722273) (19.1919191919192, 37.608407305377) (19.3939393939394, 38.2001836547291) (19.5959595959596, 38.7960412202836) (19.7979797979798, 39.3959800020406) (20, 40)