Polygons

Roundable polygons generated in 2D space. More...

Collaboration diagram for Polygons:

Files
file	polygon.scad
	Roundable polygons generated in 2D space.

Rounding
module	pg_corner_round (r=1, m=1, c=origin2d, v1=x_axis2d_uv, v2=y_axis2d_uv)
	A polygon edge round with constant radius between two vectors. More...

Round side general
module	pg_rectangle_rs (size=1, o, sr, center=false)
	A polygon rectangle with side rounding. More...

Round vertex general
module	pg_elliptical_sector (r=1, c=origin2d, v1=x_axis2d_uv, v2=x_axis2d_uv, s=true)
	A polygon elliptical sector. More...
module	pg_trapezoid (b=1, h, l=1, a=90, o=origin2d, vr, vrm=1, vfn, center=false)
	A polygon trapezoid with individual vertex rounding and arc facets. More...
module	pg_rectangle (size=1, o, vr, vrm=1, vfn, center=false)
	A polygon rectangle with vertex rounding. More...
module	pg_rhombus (size=1, o, vr, vrm=1, vfn, center=false)
	A polygon rhombus with vertex rounding. More...
module	pg_ngon (n=3, r=1, o, vr, vrm=1, vfn, center=true)
	A n-sided regular polygon with vertex rounding. More...

Round vertex triangles
module	pg_triangle_ppp (c, o, vr, vrm=1, vfn, cm=0)
	A polygon triangle specified by three coordinate points with vertex rounding. More...
module	pg_triangle_sss (v, a=x_axis_ci, o, vr, vrm=1, vfn, cm=0)
	A polygon triangle specified by three side lengths with vertex rounding. More...
module	pg_triangle_sas (v, a=x_axis_ci, o, vr, vrm=1, vfn, cm=0)
	A polygon triangle specified by size-angle-size with vertex rounding. More...
module	pg_triangle_asa (v, a=x_axis_ci, o, vr, vrm=1, vfn, cm=0)
	A polygon triangle specified by angle-size-angle with vertex rounding. More...
module	pg_triangle_aas (v, a=x_axis_ci, o, vr, vrm=1, vfn, cm=0)
	A polygon triangle specified by angle-angle-size with vertex rounding. More...

Detailed Description

Roundable polygons generated in 2D space.

Requires:
include <omdl-base.scad>;

Polygons

I	II	III
pg_corner_round()	pg_elliptical_sector()	pg_ngon()
IV	V	VI
pg_rectangle()	pg_rectangle_rs()	pg_rhombus()
VII	VIII	IX
pg_trapezoid()	pg_triangle_aas()	pg_triangle_asa()
X	XI	XII
pg_triangle_ppp()	pg_triangle_sas()	pg_triangle_sss()

Function Documentation

pg_corner_round()

module pg_corner_round	(	r	= 1,
		m	= 1,
		c	= origin2d,
		v1	= x_axis2d_uv,
		v2	= y_axis2d_uv
	)

A polygon edge round with constant radius between two vectors.

Parameters

r	<decimal> The round radius.
m	<integer> The round mode.
c	<point-2d> The round center coordinate [x, y].
v1	<line-2d | decimal> The round start angle. A 2d line, vector, or decimal angle 1.
v2	<line-2d | decimal> The round end angle. A 2d line, vector, or decimal angle 2.
fn	<integer> The number of facets (optional).
cw	<boolean> The coordinate point ordering.

Returns

<coords-2d> A list of coordinates points [[x, y], ...].

Normally, angle 1 should be less than angle 2. The edge coordinates will start at angle 1, end at angle 2, and will have radius r along a rounded transition from edge 1 to 2. When cw = true the coordinates will start at edge 1 and increase toward edge 2. When cw = false this ordering is reversed.

The round mode may be one of the following:

mode	name	description
1	fillet	fillet from one edge to the next
2	round	round from one edge to the next
3	chamfer	bevel from one edge to the next

Object example

      pg_corner_round( r=20, v1=[1,1], v2=135 );

pg_corner_round

Definition at line 563 of file polygon.scad.

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pg_elliptical_sector()

module pg_elliptical_sector	(	r	= 1,
		c	= origin2d,
		v1	= x_axis2d_uv,
		v2	= x_axis2d_uv,
		s	= true
	)

A polygon elliptical sector.

Parameters

r	<decimal-list-2 | decimal> The elliptical radius. A list [rx, ry] of decimals or a single decimal for (rx=ry).
c	<point-2d> The center coordinate [x, y].
v1	<line-2d | decimal> The sector angle 1. A 2d line, vector, or decimal.
v2	<line-2d | decimal> The sector angle 2. A 2d line, vector, or decimal.
s	<boolean> Use signed vector angle conversions. When false, positive angle conversion will be used.
fn	<integer> The number of facets (optional).
cw	<boolean> The coordinate point ordering.

Returns

<coords-2d> A list of coordinates points [[x, y], ...].

The coordinates will be between angle 1 and angle 2 and will be ordered clockwise. The sector sweep direction can be controlled by the sign of the angles. When fn is undefined, its value is determined by get_fn().

Object example

      pg_elliptical_sector( r=[20, 15], v1=115, v2=-115 );

pg_elliptical_sector

Definition at line 676 of file polygon.scad.

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pg_ngon()

module pg_ngon	(	n	= 3,
		r	= 1,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		center	= true
	)

A n-sided regular polygon with vertex rounding.

Parameters

n	<integer> The number of sides.
r	<decimal> The radius.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-n | decimal> The vertices rounding radius.
vrm	<integer-list-n | integer> The vertices rounding mode.
vfn	<integer-list-n | integer> The vertices arc fragment number.
center	<boolean> Center about origin.

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Object example

      pg_ngon( n=6, r=10, vr=1, center=true );

pg_ngon

Definition at line 865 of file polygon.scad.

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pg_rectangle()

module pg_rectangle	(	size	= 1,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		center	= false
	)

A polygon rectangle with vertex rounding.

Parameters

size	<decimal-list-2 | decimal> A list [x, y] of decimals or a single decimal for (x=y).
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-4 | decimal> The vertices rounding radius.
vrm	<integer-list-4 | integer> The vertices rounding mode.
vfn	<integer-list-4> The vertices arc fragment number.
center	<boolean> Center about origin.

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Object example

      pg_rectangle( size=[30,10], vr=2, center=true );

pg_rectangle

Definition at line 764 of file polygon.scad.

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pg_rectangle_rs()

module pg_rectangle_rs	(	size	= 1,
		o	,
		sr	,
		center	= false
	)

A polygon rectangle with side rounding.

Parameters

size	<decimal-list-2 | decimal> A list [x, y] of decimals or a single decimal for (x=y).
o	<point-2d> The origin offset coordinate [x, y].
sr	<decimal-list-2 | decimal> The side rounding radius.
center	<boolean> Center about origin.

The side rounding radius may be zero, positive, or negative. When positive, the rounding arc is swept clockwise. When negative, the arc is swept counter clockwise. A positive radius must be greater than the side length. The arch center point is located along a line that starts at the mid-point of the side vertices and extends perpendicularly by the radius distance. The arch is swept about the center point with constant radius from one vertex to the next.

Object example

      pg_rectangle_rs( [60,30], sr=[60,-100], center=true );

pg_rectangle_rs

Definition at line 615 of file polygon.scad.

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pg_rhombus()

module pg_rhombus	(	size	= 1,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		center	= false
	)

A polygon rhombus with vertex rounding.

Parameters

size	<decimal-list-2 | decimal> A list [x, y] of decimals or a single decimal for (x=y).
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-4 | decimal> The vertices rounding radius.
vrm	<integer-list-4 | integer> The vertices rounding mode.
vfn	<integer-list-4> The vertices arc fragment number.
center	<boolean> Center about origin.

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Object example

      pg_rhombus( size=[30, 15], vr=[3,1,3,1], center=true );

pg_rhombus

Definition at line 815 of file polygon.scad.

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pg_trapezoid()

module pg_trapezoid	(	b	= 1,
		h	,
		l	= 1,
		a	= 90,
		o	= origin2d,
		vr	,
		vrm	= 1,
		vfn	,
		center	= false
	)

A polygon trapezoid with individual vertex rounding and arc facets.

Parameters

b	<decimal-list-2 | decimal> The base lengths. A list [b1, b2] of 2 decimals or a single decimal for (b1=b2).
h	<decimal> The perpendicular height between bases.
l	<decimal> The left side leg length.
a	<decimal> The angle between the lower base and left leg.
o	<point-2d> The origin offset coordinate [x, y].
cw	<boolean> Polygon vertex ordering.

Returns

<coords-2d> A list of coordinates points [[x, y], ...].

When both h and l are specified, h has precedence. The function generates parallelograms, rectangles, and squares with the appropriate parameter assignments. See Wikipedia for more general information on trapezoids.

Parameters

vr	<decimal-list-4 | decimal> The vertices rounding radius.
vrm	<integer-list-4 | integer> The vertices rounding mode.
vfn	<integer-list-4> The vertices arc fragment number.
center	<boolean> Center origin at trapezoid centroid.

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Object example

      pg_trapezoid( b=[50,20], l=25, a=45, vr=2, center=true);

pg_trapezoid

Definition at line 715 of file polygon.scad.

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pg_triangle_aas()

module pg_triangle_aas	(	v	,
		a	= x_axis_ci,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		cm	= 0
	)

A polygon triangle specified by angle-angle-size with vertex rounding.

Parameters

v	<decimal-list-3> A list, [a1, a2, s1], a side length, one adjacent and the opposite angle.
a	<integer> The triangle side alignment axis index < x_axis_ci | y_axis_ci >.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-3 | decimal> The vertices rounding radius.
vrm	<integer-list-3 | integer> The vertices rounding mode.
vfn	<integer-list-3 | integer> The vertices arc fragment number.
cm	<integer> The center mode; [0,1,2, or 3].

cm	value description
0	origin at vertex v1
1	origin at triangle centroid
2	origin at triangle incenter
3	origin at triangle circumcenter

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Parameter location

aas

Object example

      pg_triangle_aas( v=[30,40,25], vr=1, cm=1);

pg_triangle_aas

Definition at line 1233 of file polygon.scad.

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pg_triangle_asa()

module pg_triangle_asa	(	v	,
		a	= x_axis_ci,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		cm	= 0
	)

A polygon triangle specified by angle-size-angle with vertex rounding.

Parameters

v	<decimal-list-3> A list, [a1, s3, a2], the side length and two adjacent angles.
a	<integer> The triangle side alignment axis index < x_axis_ci | y_axis_ci >.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-3 | decimal> The vertices rounding radius.
vrm	<integer-list-3 | integer> The vertices rounding mode.
vfn	<integer-list-3 | integer> The vertices arc fragment number.
cm	<integer> The center mode; [0,1,2, or 3].

cm	value description
0	origin at vertex v1
1	origin at triangle centroid
2	origin at triangle incenter
3	origin at triangle circumcenter

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Parameter location

asa

Object example

      pg_triangle_asa( v=[60,30,25], vr=1, cm=1);

pg_triangle_asa

Definition at line 1168 of file polygon.scad.

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pg_triangle_ppp()

module pg_triangle_ppp	(	c	,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		cm	= 0
	)

A polygon triangle specified by three coordinate points with vertex rounding.

Parameters

c	<coords-list-3> A list, [v1, v2, v3], the vertex coordinates in 2d.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-3 | decimal> The vertices rounding radius.
vrm	<integer-list-3 | integer> The vertices rounding mode.
vfn	<integer-list-3 | integer> The vertices arc fragment number.
cm	<integer> The center mode; [0,1,2, or 3].

cm	value description
0	origin at vertex v1
1	origin at triangle centroid
2	origin at triangle incenter
3	origin at triangle circumcenter

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Parameter location

ppp

Object example

      pg_triangle_ppp( c=[[-15,-5],[10,15], [10,-10]], vr=1 );

pg_triangle_ppp

Definition at line 966 of file polygon.scad.

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pg_triangle_sas()

module pg_triangle_sas	(	v	,
		a	= x_axis_ci,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		cm	= 0
	)

A polygon triangle specified by size-angle-size with vertex rounding.

Parameters

v	<decimal-list-3> A list, [s1, a3, s2], the side lengths and the included angle.
a	<integer> The triangle side alignment axis index < x_axis_ci | y_axis_ci >.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-3 | decimal> The vertices rounding radius.
vrm	<integer-list-3 | integer> The vertices rounding mode.
vfn	<integer-list-3 | integer> The vertices arc fragment number.
cm	<integer> The center mode; [0,1,2, or 3].

cm	value description
0	origin at vertex v1
1	origin at triangle centroid
2	origin at triangle incenter
3	origin at triangle circumcenter

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Parameter location

sas

Object example

      pg_triangle_sas( v=[15,30,20], vr=1, cm=1);

pg_triangle_sas

Definition at line 1103 of file polygon.scad.

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pg_triangle_sss()

module pg_triangle_sss	(	v	,
		a	= x_axis_ci,
		o	,
		vr	,
		vrm	= 1,
		vfn	,
		cm	= 0
	)

A polygon triangle specified by three side lengths with vertex rounding.

Parameters

v	<decimal-list-3> A list, [s1, s2, s3], the side lengths.
a	<integer> The triangle side alignment axis index < x_axis_ci | y_axis_ci >.
o	<point-2d> The origin offset coordinate [x, y].
vr	<decimal-list-3 | decimal> The vertices rounding radius.
vrm	<integer-list-3 | integer> The vertices rounding mode.
vfn	<integer-list-3 | integer> The vertices arc fragment number.
cm	<integer> The center mode; [0,1,2, or 3].

cm	value description
0	origin at vertex v1
1	origin at triangle centroid
2	origin at triangle incenter
3	origin at triangle circumcenter

Each vertex may be assigned an individual rounding radius, rounding mode, and facet number as described in polygon_round_eve_all_p by using the parameters: vr, vrm, and vfn. When vr is undefined, no rounding is performed on the polygon vertices.

Parameter location

sss

Object example

      pg_triangle_sss( v=[10,20,25], vr=1, cm=1);

pg_triangle_sss

Definition at line 1038 of file polygon.scad.

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