Graphics Render Examples

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Graphics Render Examples

Line and Triangle Examples

Points connecting two intersecting lines at an angle (or two sides of a triangle). Three sets of point coordinates for lines are generated with the function POLYPOINTS() and the lines are split to 10 segments to have ten points for each of the three line sets. Two lines are connected with the point sets on the lines diagonally opposite points

Lines3-1.jpg 
pointcoords=POLYPOINTS(3,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[1])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[2])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[0])).m(r=>r.flatten())
var d=	[
		["type","coordinates","count"],
		["line",lines1,lines1.length],
	]
RENDER(d) ""

Lines are connected with the point sets on the lines diagonally opposite all three line sets

Lines3-3.jpg 
pointcoords=POLYPOINTS(3,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[2])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[0])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[1])).m(r=>r.flatten())
var d=	[	["type","coordinates","count"],
		["line",lines1,lines1.length],
		["line",lines2,lines2.length],
		["line",lines3,lines3.length]	]
RENDER(d) ""

Four sets of point coordinates for lines are generated with the function POLYPOINTS() and the lines are split to 10 segments to have ten points for each of the four line sets. Lines are rendered with the set of points and the type of object to render, given to the RENDER function.

Lines-poly4-lines0.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[1])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[2])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[3])).m(r=>r.flatten())
lines4=(s[3].rowpush(s[0])).m(r=>r.flatten())
var d=	[
		["type","coordinates","count"],
		["line",lines1,lines1.length]
	]

RENDER(d) 
""

Two adjacent line sets are connected and rendered in this example.

Lines-poly4-lines12.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[1])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[2])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[3])).m(r=>r.flatten())
lines4=(s[3].rowpush(s[0])).m(r=>r.flatten())
var d=	[	["type","coordinates","count"],
		["line",lines1,lines1.length],
		["line",lines2,lines2.length] 	
	]

RENDER(d) 
""

Four adjacent line sets are connected and rendered in this example.

Lines-poly4-lines01234.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[1])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[2])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[3])).m(r=>r.flatten())
lines4=(s[3].rowpush(s[0])).m(r=>r.flatten())
var d=	[	["type","coordinates","count"],
		["line",lines1,lines1.length],
		["line",lines2,lines2.length],
		["line",lines3,lines3.length],
		["line",lines4,lines4.length]	]

RENDER(d)
""

Just two opposite side point sets connected and rendered in this example.

Lines-poly4-cage0.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)

lines1=(s[0].rowpush(s[2])).m(r=>r.flatten())
lines2=(s[2].rowpush(s[0])).m(r=>r.flatten())
lines3=(s[1].rowpush(s[2])).m(r=>r.flatten())
var d=	[
		["type","coordinates","count"],
		["line",lines2,lines2.length]
	]

RENDER(d)
""

Two adjacent and two opposite lines point sets connected and rendered in this example.

Lines-poly4-lines1+cage0.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[2])).m(r=>r.flatten())
lines2=(s[2].rowpush(s[0])).m(r=>r.flatten())
lines3=(s[1].rowpush(s[2])).m(r=>r.flatten())
var d=	[
			["type","coordinates","count"],
			["line",lines1,lines1.length],
			["line",lines2,lines2.length],
			["line",lines3,lines3.length]
		]
RENDER(d)
""

Four line sets and lines across are connected and rendered in this example.

Lines-poly4-lines01234+cage0213.jpg 
pointcoords=POLYPOINTS(4,100,100);
s=LINESPLIT(pointcoords,10,true)
lines1=(s[0].rowpush(s[1])).m(r=>r.flatten())
lines2=(s[1].rowpush(s[2])).m(r=>r.flatten())
lines3=(s[2].rowpush(s[3])).m(r=>r.flatten())
lines4=(s[3].rowpush(s[0])).m(r=>r.flatten())
lines5=(s[2].rowpush(s[0])).m(r=>r.flatten())
lines6=(s[1].rowpush(s[3])).m(r=>r.flatten())
var d=	[
		["type","coordinates","count"],
		["line",lines1,lines1.length],
		["line",lines2,lines2.length],
		["line",lines3,lines3.length],
		["line",lines4,lines4.length],	
		["line",lines5,lines5.length],
		["line",lines6,lines6.length]
	]

RENDER(d)
""


Cardioid Examples

Following the "the midpoints of the circles lie on the perimeter of the fixed generator circle" method to draw a cardioid:

1) Choose a circle c and a point p on its perimeter, 2) Draw circles containing point p with centers on the perimeter of circle c

Example 1

Cycloid (fig.1)
numpoints = 50;
pts=MAKEPOLYGONPOINTS(numpoints,[50,50],[200,200], 270)
start=pts[0];
circlesat=
	pts
	   .map(
		   p=>[p[0],p[1],SQRT(POWER(p[0]-start[0],2)+POWER(p[1]-start[1],2))]
	       )
RENDER(	[
	   ["type","cx","cy","r","stroke","stroke-width","count"],
	   ["circle",circlesat.column(0),circlesat.column(1),circlesat.column(2),"red",1,circlesat.length]
	] 
      )""

Example 2

Rendering two cardioid. A smaller and a larger one.

Two Cycloids (fig.2)
numpoints = 50;
pts=MAKEPOLYGONPOINTS(numpoints,[30,50],[200,200], 150)
start=pts[0];
circlesat1=
	pts
	   .map(
		   p=>[p[0],p[1],SQRT(POWER(p[0]-start[0],2)+POWER(p[1]-start[1],2))]
	       )
pts=MAKEPOLYGONPOINTS(numpoints,[70,70],[500,200], 0)
start=pts[0];
circlesat2=
	pts
	   .map(
		   p=>[p[0],p[1],SQRT(POWER(p[0]-start[0],2)+POWER(p[1]-start[1],2))]
	       )
cycloids = RENDER([
	      ["id","type","cx","cy","r","stroke","stroke-width","count"],
	      ["cycloid1","circle",circlesat1.column(1),circlesat1.column(0),circlesat1.column(2),"red",1,circlesat1.length],
	      ["cycloid2","circle",circlesat2.column(1),circlesat2.column(0),circlesat2.column(2),"red",1,circlesat2.length]
	   ] );""
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