105 lines
3.5 KiB
Text
105 lines
3.5 KiB
Text
// Adpated from non recursive sierpinsky.bas for SmallBASIC 0.12.6 [B+=MGA] 2016-05-19 with demo mod 2016-05-29
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//Sierpinski triangle gasket drawn with lines from any 3 given points
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// WITHOUT RECURSIVE Calls
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//first a sub, given 3 points of a triangle draw the traiangle within
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//from the midpoints of each line forming the outer triangle
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//this is the basic Sierpinski Unit that is repeated at greater depths
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//3 points is 6 arguments to function plus a depth level
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xmax=800:ymax=600
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open window xmax,ymax
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backcolor 0,0,0
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color 255,0,0
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clear window
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sub SierLineTri(x1, y1, x2, y2, x3, y3, maxDepth)
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local mx1, mx2, mx3, my1, my2, my3, ptcount, depth, i, X, Y
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Y = 1
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//load given set of 3 points into oa = outer triangles array, ia = inner triangles array
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ptCount = 3
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depth = 1
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dim oa(ptCount - 1, 1) //the outer points array
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oa(0, X) = x1
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oa(0, Y) = y1
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oa(1, X) = x2
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oa(1, Y) = y2
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oa(2, X) = x3
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oa(2, Y) = y3
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dim ia(3 * ptCount - 1, 1) //the inner points array
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iaIndex = 0
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while(depth <= maxDepth)
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for i=0 to ptCount-1 step 3 //draw outer triangles at this level
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if depth = 1 then
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line oa(i,X), oa(i,Y), oa(i+1,X), oa(i+1,Y)
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line oa(i+1,X), oa(i+1,Y), oa(i+2,X), oa(i+2,Y)
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line oa(i,X), oa(i,Y), oa(i+2,X), oa(i+2,Y)
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end if
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if oa(i+1,X) < oa(i,X) then mx1 = (oa(i,X) - oa(i+1,X))/2 + oa(i+1,X) else mx1 = (oa(i+1,X) - oa(i,X))/2 + oa(i,X) endif
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if oa(i+1,Y) < oa(i,Y) then my1 = (oa(i,Y) - oa(i+1,Y))/2 + oa(i+1,Y) else my1 = (oa(i+1,Y) - oa(i,Y))/2 + oa(i,Y) endif
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if oa(i+2,X) < oa(i+1,X) then mx2 = (oa(i+1,X)-oa(i+2,X))/2 + oa(i+2,X) else mx2 = (oa(i+2,X)-oa(i+1,X))/2 + oa(i+1,X) endif
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if oa(i+2,Y) < oa(i+1,Y) then my2 = (oa(i+1,Y)-oa(i+2,Y))/2 + oa(i+2,Y) else my2 = (oa(i+2,Y)-oa(i+1,Y))/2 + oa(i+1,Y) endif
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if oa(i+2,X) < oa(i,X) then mx3 = (oa(i,X) - oa(i+2,X))/2 + oa(i+2,X) else mx3 = (oa(i+2,X) - oa(i,X))/2 + oa(i,X) endif
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if oa(i+2,Y) < oa(i,Y) then my3 = (oa(i,Y) - oa(i+2,Y))/2 + oa(i+2,Y) else my3 = (oa(i+2,Y) - oa(i,Y))/2 + oa(i,Y) endif
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//color 9 //testing
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//draw all inner triangles
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line mx1, my1, mx2, my2
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line mx2, my2, mx3, my3
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line mx1, my1, mx3, my3
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//x1, y1 with mx1, my1 and mx3, my3
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ia(iaIndex,X) = oa(i,X)
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ia(iaIndex,Y) = oa(i,Y) : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx1
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ia(iaIndex,Y) = my1 : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx3
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ia(iaIndex,Y) = my3 : iaIndex = iaIndex + 1
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//x2, y2 with mx1, my1 and mx2, my2
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ia(iaIndex,X) = oa(i+1,X)
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ia(iaIndex,Y) = oa(i+1,Y) : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx1
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ia(iaIndex,Y) = my1 : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx2
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ia(iaIndex,Y) = my2 : iaIndex = iaIndex + 1
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//x3, y3 with mx3, my3 and mx2, my2
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ia(iaIndex,X) = oa(i+2,X)
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ia(iaIndex,Y) = oa(i+2,Y) : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx2
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ia(iaIndex,Y) = my2 : iaIndex = iaIndex + 1
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ia(iaIndex,X) = mx3
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ia(iaIndex,Y) = my3 : iaIndex = iaIndex + 1
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next i
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//update and prepare for next level
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ptCount = ptCount * 3
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depth = depth + 1
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redim oa(ptCount - 1, 1 )
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for i = 0 to ptCount - 1
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oa(i, X) = ia(i, X)
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oa(i, Y) = ia(i, Y)
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next i
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redim ia(3 * ptCount - 1, 1)
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iaIndex = 0
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wend
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end sub
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//Test Demo for the sub (NEW as 2016 - 05 - 29 !!!!!)
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cx=xmax/2
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cy=ymax/2
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r=cy - 20
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N=3
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for i = 0 to 2
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color 64+42*i,64+42*i,64+42*i
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SierLineTri(cx, cy, cx+r*cos(2*pi/N*i), cy +r*sin(2*pi/N*i), cx + r*cos(2*pi/N*(i+1)), cy + r*sin(2*pi/N*(i+1)), 5)
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next i
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