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Help to translate this system of cords[mathematic] problem

 
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Twistedfate
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PostPosted: Fri May 05, 2017 3:01 pm    Post subject: Help to translate this system of cords[mathematic] problem Reply with quote
I want you to make equation to calculate (x,y) from Longitudinal and Transverse lines .


(x,y) → the red numbers
blue numbers → Longitudinal cords
light blue →Transverse cords
the center cords (x51,y51) (1648,3072)

X and y full.jpg
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X and y full.jpg
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mgr.inz.Player
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Location: W kraju nad Wisla. UTC+01:00
PostPosted: Fri May 05, 2017 8:55 pm    Post subject: This post has 1 review(s) Reply with quote
Code:
function firstTransform(x,y)
  -- reflect at y=3072
  -- -(y-3072)+3072=-y+3072+3072=6144-y
  y=6144-y

  --scale x by 2
  x=2*x

  --rot 45° ccw at {2*1648 , 3072}
  local a,b=(2*1648),3072
  local t=1/(2^0.5)
  x,y = x-a, y-b
  return t*x - t*y + a, t*x + t*y + b
end

ScaleFirstTransform_scale=nil
function ScaleFirstTransform(xx,yy)

  if ScaleFirstTransform_scale==nil then
    -- point1 (1040,3072) -> (32,32)
    local x1,y1=firstTransform(1040,3072)

    -- point3 (2256,3072) -> (70,70)
    local x3,y3=firstTransform(2256,3072)

    --scale for x:
    local ax = 38/(x3-x1)  -- 70-32 = 38
    local bx = 32-x1*ax

    --scale for y:
    local ay = 38/(y3-y1)  -- 70-32 = 38
    local by = 32-y1*ay

    ScaleFirstTransform_scale = {{ax,bx},{ay,by}}
  end

  local t=ScaleFirstTransform_scale

  local x,y = firstTransform(xx,yy)
  return x*t[1][1]+t[1][2],y*t[2][1]+t[2][2]
end

function TwistedfateTransform(x,y)
  return ScaleFirstTransform(x,y)
end

print('tests:')
print('(1040,3072) -> (32,32), we get:',TwistedfateTransform(1040,3072))
print('(1648,1856) -> (32,70), we get:',TwistedfateTransform(1648,1856))
print('(2256,3072) -> (70,70), we get:',TwistedfateTransform(2256,3072))
print('(1648,4288) -> (70,32), we get:',TwistedfateTransform(1648,4288))

print('(1344,2464) -> (32,51), we get:',TwistedfateTransform(1344,2464))
print('(1344,3680) -> (51,32), we get:',TwistedfateTransform(1344,3680))
print('(1952,2464) -> (51,70), we get:',TwistedfateTransform(1952,2464))
print('(1952,3680) -> (70,51), we get:',TwistedfateTransform(1952,3680))

print('(1648,3072) -> (51,51), we get:',TwistedfateTransform(1648,3072))

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Twistedfate
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Joined: 11 Mar 2016
Posts: 231
PostPosted: Sat May 06, 2017 2:15 am    Post subject: Reply with quote
Wink Wink
Thank you ! Thank you ! Thank you ! Thank you ! Thank you !
its read perfect !!
is there any reference you used to solve that ?
I didn't expect any one to solve it <3 .
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mgr.inz.Player
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Location: W kraju nad Wisla. UTC+01:00
PostPosted: Sat May 06, 2017 5:29 pm    Post subject: Reply with quote
Some time ago I made similar 2D transformations.
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