Code archives/Algorithms/Rotated ellipse
This code has been declared by its author to be Public Domain code.
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| Bresenham like code for rotated ellipses Uses crunches huge numbers more than can be handled which introduces the jumpy bug at some sizes.. But it produces silky smooth ellipses, which is rather scarce to see these days. | |||||
Graphics 800,600,16,2:SetBuffer BackBuffer()
Repeat:Cls:xx=MouseX():yy=MouseY()
Color 0,255,0:ellipse(512,384,1+yy/2.0,200,xx/200.0)
Color 255,255,255:Plot 512,384:Plot 512+100,384:Plot 512-100,384:Plot 512,384+200:Plot 512,384-200
Flip
Until MouseDown(2)
Function ellipse (iXC#,iYC#,A#,B#,angle#)
;
; General ellipse
;
; Known bugs:
; jumpy movement sometimes, as it uses huge numbers, too large To fit storage
; It has few lines with trigonometry, these could very possibly be replaced with integer table or
; tables of degrees Or similiar. It wraps the angle into an acceptable range, and sets xflag accordingly.
;
R2D# = 180.0/Pi:D2R# = Pi/180.0
If angle# < Pi/2.0
xflag#=1
ElseIf angle#>Pi/2 And angle#<Pi
temp#=angle#-Pi/2.0:angle#=Pi/2.0-temp#:xflag#=-1
ElseIf angle#>=Pi And angle#<Pi*1.5
angle#=angle#-Pi:xflag#=1
ElseIf angle#>=Pi*1.5 And angle#<Pi*2.0
angle#=angle#-Pi:temp#=angle#-Pi/2.0:angle#=Pi/2.0-temp#:xflag#=-1
EndIf
; ...To output these 4 integer points. (and the said xflag), These are where major and minor axis of ellipse ends (determines shape as in aligned axis algorithms).
ixa#=Int(Cos(angle#*R2D#)*A#)
iya#=Int(Sin(angle#*R2D#)*A#)
ixb#=Int(Cos((angle#+(Pi/2.0))*R2D#)*B#)
iyb#=Int(Sin((angle#+(Pi/2.0))*R2D#)*B#)
; rest of code uses only variables:
; ixa,iya,ixb,iyb
; ixc, iyc, xflag
; these are as every one else from now on, integers
Plot ixc#-ixa#,iyc#-iya#
Plot ixc#-ixb#,iyc#-iyb#
Plot ixc#-ixb#,iyc#-iya#
Plot ixc#-ixa#,iyc#-iyb#
; From now on, integers only, it uses multiplication much, and needs very large integers (in large resolutions even more than 64bits)
; therefor single precision are used to alloud the space, but theres no fixed point Or floating point involved.
ixa2#=ixa#*ixa#
iya2#=iya#*iya#
ixb2#=ixb#*ixb#
iyb2#=iyb#*iyb#
ixaya#=ixa#*iya#
ixbyb#=ixb#*iyb#
ila2#=ixa2#+iya2#
ila4#=ila2#*ila2#
ilb2#=ixb2#+iyb2#
ilb4#=ilb2#*ilb2#
ia#=ixa2#*ilb4#+ixb2#*ila4#
ib#=ixaya#*ilb4#+ixbyb#*ila4#
ic#=iya2#*ilb4#+iyb2#*ila4#
id#=ila4#*ilb4#
If iYA# <= iXA#
; Start AT (-xA,-yA)
iX# = -iXA#:iY# = -iYA#:iDx# = -(iB#*iXA#+iC#*iYA#):iDy# = iA#*iXA#+iB#*iYA#
; Arc FROM (-xA,-yA) TO point (x0,y0) where dx/dy = 0
While iDx# <= 0
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iY#=iY#+1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iY#+iC#*iY#*iY#-iD#
If iSigma# < 0 Then iDx#=iDx#-iB#:iDy#=iDy#+iA#:iX#=iX#-1
iDx#=iDx# + iC#
iDy#=iDy# - iB#
Wend
; Arc FROM (x0,y0) TO point (x1,y1) where dy/dx = 1
While iDx# <= iDy#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iY#=iY#+1
iXp1# = iX#+1
iSigma# = iA#*iXp1#*iXp1#+2*iB#*iXp1#*iY#+iC#*iY#*iY#-iD#
If iSigma# >= 0 Then iDx#=iDx# + iB#:iDy#=iDy# - iA#:iX# = iXp1#
iDx#=iDx# + iC#
iDy#=iDy# - iB#
Wend
; Arc FROM (x1,y1) TO point (x2,y2) where dy/dx = 0
While iDy# >= 0
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iX=iX+1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iY#+iC#*iY#*iY#-iD#
If iSigma# < 0 Then iDx#=iDx# + iC# : iDy#=iDy# - iB# : iY#=iY#+1
iDx#=iDx# + iB#
iDy#=iDy# - iA#
Wend
; Arc FROM (x2,y2) TO point (x3,y3) where dy/dx = -1
While iDy# >= -iDx#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iX#=iX#+1
iYm1# = iY#-1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iYm1#+iC#*iYm1#*iYm1#-iD#
If iSigma# >= 0 Then iDx#=iDx# - iC#:iDy#=iDy# + iB#:iY# = iYm1#
iDx#=iDx# + iB#
iDy#=iDy# - iA#
Wend
; Arc FROM (x3,y3) TO (xa,ya)
While iY# >= iYA#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iY#=iY#-1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iY#+iC#*iY#*iY#-iD#
If iSigma# < 0 Then iDx#=iDx# + iB#:iDy#=iDy# - iA#:iX#=iX#+1
iDx#=iDx# - iC#
iDy#=iDy# + iB#
Wend
Else
; Start AT (-xa,-ya)
iX# = -iXA#:iY# = -iYA#:iDx# = -(iB#*iXA#+iC#*iYA#):iDy# = iA#*iXA#+iB#*iYA#
; Arc FROM (-xa,-ya) TO point (x0,y0) where dy/dx = -1
While -iDx# >= iDy#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iX#=iX#-1
iYp1# = iY#+1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iYp1#+iC#*iYp1#*iYp1#-iD#
If iSigma# >= 0 Then iDx#=iDx# + iC# : iDy#=iDy# - iB#:iY# = iYp1#
iDx#=IDx# - iB#
iDy#=Idy# +iA#
Wend
; Arc FROM (x0,y0) TO point (x1,y1) where dx/dy = 0
While iDx# <= 0
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iY#=iY#+1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iY#+iC#*iY#*iY#-iD#
If iSigma# < 0 Then iDx#=iDx# - iB#:iDy#=iDy# + iA#:iX#=iX#-1
iDx#=iDx# + iC#
iDy#=iDy# - iB#
Wend
; Arc FROM (x1,y1) TO point (x2,y2) where dy/dx = 1
While iDx# <= iDy#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iY#=iY#+1
iXp1# = iX#+1
iSigma# = iA#*iXp1#*iXp1#+2*iB#*iXp1#*iY#+iC#*iY#*iY#-iD#
If iSigma# >= 0 Then iDx#=IDx# + iB# :iDy#=Idy# - iA# : iX# = iXp1#
iDx#=iDx# + iC#
iDy#=iDy# - iB#
Wend
; Arc FROM (x2,y2) TO point (x3,y3) where dy/dx = 0
While iDy# >= 0
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iX#=iX#+1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iY#+iC#*iY#*iY#-iD#
If iSigma# < 0 Then iDx#=iDx# + iC# : iDy#=iDy# - iB# : iY#=iY#+1
iDx#=iDx# + iB#
iDy#=iDy# - iA#
Wend
; Arc FROM (x3,y3) TO (xa,ya)
While iX# <= iXA#
Plot iXC#+iX#*xflag#,iYC#+iY#
Plot iXC#-iX#*xflag#,iYC#-iY#
iX#=iX#+1
iYm1# = iY#-1
iSigma# = iA#*iX#*iX#+2*iB#*iX#*iYm1#+iC#*iYm1#*iYm1#-iD#
If iSigma# >= 0 Then iDx#=iDx# - iC# : iDy#=iDy# + iB# :iY# = iYm1#
iDx#=iDx# + iB#
iDy#=iDy# - iA#
Wend
EndIf
End Function |
Comments
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| Nice algo Jimmy! Here's a version that uses WritePixelFast to speed up the drawing part of this algorithm. WritePixelFast gives it a 50X speed boost! This version of Jimmy's rotated ellipse is slightly faster than the intrinsic BlitzPlus/Blitz3D "Oval" function which is NOT rotated. |
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| This is good but what about a filled rotated oval? Jim |
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