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- dx = x1-x2
- dy = y1-y2
- dist = sqrt(dx*dx + dy*dy)
- dx /= dist
- dy /= dist
- x3 = x1 + (N/2)*dy
- y3 = y1 - (N/2)*dx
- x4 = x1 - (N/2)*dy
- y4 = y1 + (N/2)*dx
- vx = x2-x1
- vy = y2-y1
- len = sqrt( vx*vx + vy*vy )
- ux = -vy/len
- uy = vx/len
- x3 = x1 + N/2 * ux
- Y3 = y1 + N/2 * uy
- x4 = x1 - N/2 * ux
- Y4 = y1 - N/2 * uy
- in: line_length, cap_length, rotation, position of line centre
- define points:
- tl (-line_length/2, cap_length)
- tr (line_length/2, cap_length)
- bl (-line_length/2, -cap_length)
- br (line_length/2, -cap_length)
- rotate the four points by 'rotation'
- offset four points by 'position'
- drawline (midpoint tl,bl to midpoint tr,br)
- drawline (tl to bl)
- drawline (tr to br)
- while x21 is negative, y13 will be positive
- while x21 is positive, y13 will be negative
- while y21 is positive, x13 will be positive
- while y21 is negative, x13 will be negative
- x21 = x1 - x2
- y21 = y1 - y2
- x13^2 + y13^2 = |1->3|^2
- x13^2 + y13^2 = (N/2)^2
- x21*x13 + y21*y13 = 2->1 dot 1->3
- x21*x13 + y21*y13 = 0
- x21*x13 = -y21*y13
- x13 = -(y21/x21)y13
- x13 = -phi*y13
- plug x13 into a
- phi^2*y13^2 + y13^2 = |1->3|^2
- factor out y13
- y13^2 * (phi^2 + 1) =
- plug in phi
- y13^2 * (y21^2/x21^2 + 1) =
- multiply both sides by x21^2
- y13^2 * (y21^2 + x21^2) = |1->3|^2 * x21^2
- plug in Pythagorean theorem of 2->1
- y13^2 * |2->1|^2 = |1->3|^2 * x21^2
- take square root of both sides
- y13 * |2->1| = |1->3| * x21
- divide both sides by the length of 1->2
- y13 = (|1->3|/|2->1|) *x21
- lets call the ratio of 1->3 to 2->1 lengths psi
- y13 = psi * x21
- check the signs
- when x21 is negative, y13 will be positive
- when x21 is positive, y13 will be negative
- y13 = -psi * x21
- plug y13 into a
- x13^2 + x13^2/phi^2 = |1->3|^2
- factor out x13
- x13^2 * (1 + 1/phi^2) =
- plug in phi
- x13^2 * (1 + x21^2/y21^2) =
- multiply both sides by y21^2
- x13^2 * (y21^2 + x21^2) = |1->3|^2 * y21^2
- plug in Pythagorean theorem of 2->1
- x13^2 * |2->1|^2 = |1->3|^2 * y21^2
- take square root of both sides
- x13 * |2->1| = |1->3| * y21
- divide both sides by the length of 2->1
- x13 = (|1->3|/|2->1|) *y21
- lets call the ratio of |1->3| to |2->1| psi
- x13 = psi * y21
- check the signs
- when y21 is negative, x13 will be negative
- when y21 is positive, x13 will be negative
- x13 = psi * y21
- x21 = x1 - x2
- y21 = y1 - y2
- |2->1| = sqrt( x21^2 + y^21^2 )
- |1->3| = N/2
- psi = |1->3|/|2->1|
- y13 = -psi * x21
- x13 = psi * y21
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