Ah, I see. "Intersecting circles" on google gave me some interesting mathematical information.
I think for the meshpainting program, the main issues are: (1) the triangles are not stretched.
(2) the triangles do not overlap.
So if my distance-based idea fails I'll go for a simpler solution and arrange the (normalized, facing front) triangles by their index number from left to right and top-down.
It has a few small disadvantages, but it is a workable (and less complex) solution.
But first, I will study a bit more on this.
For anyone interested, here is the code I wrote for computing the (two) intersection points of two circles.
Input:
x, y coordinates for point A, B and D
distance AB, AC, BC, CD
Output:
cx, cy
I think for the meshpainting program, the main issues are: (1) the triangles are not stretched.
(2) the triangles do not overlap.
So if my distance-based idea fails I'll go for a simpler solution and arrange the (normalized, facing front) triangles by their index number from left to right and top-down.
It has a few small disadvantages, but it is a workable (and less complex) solution.
But first, I will study a bit more on this.
For anyone interested, here is the code I wrote for computing the (two) intersection points of two circles.
Input:
x, y coordinates for point A, B and D
distance AB, AC, BC, CD
Output:
cx, cy
Open in online IDE;--------------------------------------------------------------------------------------------------- ; C2 ; /\ ; / \ ; / \ ; A __________ B ; \ / ; \ / ; \/ ; C1 . D ; ; this program calculates (X,Y) of point C1/C2, ; given are the coordinates of point A, B and D. ; also known are the distances between each point. ;--------------------------------------------------------------------------------------------------- ;declare float variables Local mx#, my# Local ax#, ay#, bx#, by#, dx#, dy# Local cx1#, cy1#, cx2#, cy2# Local oax#, oay#, obx#, oby#, ocx#, ocy# Local organgle#, distance# Local h1#, d1#, h2#, d2#, h3#, d3# Local AB#, BC#, AC#, CD# Local C1#, C2# ;--------------------------------------------------------------------------------------------------- ; Main Program ;--------------------------------------------------------------------------------------------------- ;setup Graphics 320, 240 SetBuffer BackBuffer() SeedRnd MilliSecs() ;main loop Repeat Cls Locate 0, 0 ;----- ;INPUT ;----- ;generate three points ax = Rand(250) + 35 ay = Rand(80) + 120 bx = Rand(250) + 35 by = Rand(80) + 120 cx = Rand(250) + 35 cy = Rand(80) + 120 ;this point is used to determine which ;of the two points is valid by checking the distance dx = Rand(250) + 35 dy = Rand(80) + 120 ;calculate their distances AC = VDist(ax, ay, cx, cy) AB = VDist(ax, ay, bx, by) BC = VDist(bx, by, cx, cy) CD = VDist(cx, cy, dx, dy) ;------- ;PROCESS ;------- ;----------------------------------------------------- ;goal - (re)calculate the position of point C (cx, cy) ;----------------------------------------------------- ;store the position of point A, for translate purposes oax = ax oay = ay ;and point B and C as well for drawing purposes obx = bx oby = by ocx = cx ocy = cy ;calculate angle and distance from A to B organgle = (450 - ATan2(bx - ax, by - ay)) Mod 360 distance = vdist(ax, ay, bx, by) ;set new coordinates A and B (0,0)-(AB,0) ;because the formula works only with points A and B aligned on the X-axis. (y=0) ax = 0 ay = 0 bx = distance by = 0 ;---------------------------------------------------------------------------------- ; this is the main formula ; it calculates (x,y) for ; the third point ;there is two possibilities: C1 and C2 ;---------------------------------------------------------------------------------- cx1 = ((AB ^ 2) - (BC ^ 2) + (AC ^ 2)) / (2 * AB) cy1 = Sqr(((4 * AB ^ 2 * AC ^ 2) - (AB ^ 2 - BC ^ 2 + AC ^ 2) ^ 2) / (4 * AB ^ 2)) cx2 = cx1 cy2 = -cy1 ;----------------------------------------------------------------------------------- ; using the 4th point (D) we could determine which option is valid ;----------------------------------------------------------------------------------- Color 0, 0, 255 Rect 0, 0, 320, 40 Color 255, 255, 255 ;;check distances(lengths) Print "AB=" + vdist(ax, ay, bx, by) + " (" + AB + ")" Print "BC=" + vdist(bx, by, cx1, cy1) + " (" + BC + ")" Print "AC=" + vdist(ax, ay, cx1, cy1) + " (" + AC + ")" ;calculate midpoint 1 mx1 = (ax + bx + cx1) / 3 my1 = (ay + by + cy1) / 3 ;calculate angles (h1,h2,h3,h4) and distances (d1,d2,d3,d4) ;point A h1 = 450 - ATan2((ax - mx1), (ay - my1)) d1 = vdist(ax, ay, mx1, my1) ;point B h2 = 450 - ATan2((bx - mx1), (by - my1)) d2 = vdist(bx, by, mx1, my1) ;point C1 h3 = 450 - ATan2((cx1 - mx1), (cy1 - my1)) d3 = vdist(cx1, cy1, mx1, my1) ;point C2 h4 = 450 - ATan2((cx2 - mx1), (cy2 - my1)) d4 = vdist(cx2, cy2, mx1, my1) ;AB are rotated back into their original position ;C1 and C2 rotate along ax = Cos(h1 + organgle) * d1 ay = Sin(h1 + organgle) * d1 bx = Cos(h2 + organgle) * d2 by = Sin(h2 + organgle) * d2 cx1 = Cos(h3 + organgle) * d3 cy1 = Sin(h3 + organgle) * d3 cx2 = Cos(h4 + organgle) * d4 cy2 = Sin(h4 + organgle) * d4 ;translate points so that point A is at it's original position cx2 = cx2 - ax + oax cy2 = cy2 - ay + oay cx1 = cx1 - ax + oax cy1 = cy1 - ay + oay bx = bx - ax + oax by = by - ay + oay ax = ax - ax + oax ay = ay - ay + oay ;determine what C is valid If Abs(VDist(cx1, cy1, dx, dy) - CD) < Abs(VDist(cx2, cy2, dx, dy) - CD) Then cx = cx1 cy = cy1 Else cx = cx2 cy = cy2 End If ;------ ;OUTPUT ;------ Viewport 0, 40, 320, 200 Color 0, 64, 0 ;draw original points to the screen Oval oax - 3, oay - 3, 7, 7, False Oval obx - 3, oby - 3, 7, 7, False Oval ocx - 3, ocy - 3, 7, 7, False ;draw reference point D Oval dx - 2, dy - 2, 5, 5, False ;draw triangle Color 64, 64, 0 Line ax, ay, bx, by Line bx, by, cx, cy Line cx, cy, ax, ay ;text labels Color 180, 180, 180 Text ax, ay, "A", True, False Text bx, by, "B", True, False Text dx, dy, "D", True, False Color 255, 0, 0 Text cx, cy, "C", True, False Viewport 0, 0, GraphicsWidth(), GraphicsHeight() Flip ;wait for a key now = MilliSecs() Repeat Delay 50 Until (MilliSecs() - now > 750) Or KeyDown(1) Or KeyDown(205) Until KeyHit(1) End ;--------------------------------------------------------------------------------------------------- ; END ;--------------------------------------------------------------------------------------------------- ;---------------------------------------------------------------------------------------------------- ; VDist() ;---------------------------------------------------------------------------------------------------- ;return distance between two points Function VDist#(x1#, y1#, x2#, y2#) Return Sqr((x2 - x1) ^ 2 + (y2 - y1) ^ 2) End Function