I think the dL_i(x+1, y) and dL_i(x, y+1) notations are confusing. Is it better to use L_i(x+1, y) = L_i(x, y) + dY_i = L_i(x, y) + A_i and L_i(x, y+1) = L_i(x, y) + dX_i = L_i(x, y) + B_i instead?
sc2019
Is B_i supposed to be dX_i or -dX_i? The equation for L_i expands to dY_i * x - dY_i * X_i - dX_i * y + dX_i * Y_i, which means the coefficient for y is B_i = -dX_i. However, according to the equation for dL_i(x, y+1), dX_i = B_i. I think it needs to be changed to dL_i(x,y+1) = L_i(x,y) - dX_i.
cs1
It also interesting to see how this equation related to y = mx + b format.
Ax + By + C = 0 asserts that the point is on the edge aka on the line, so this form is equal to y =mx +b.
I think the dL_i(x+1, y) and dL_i(x, y+1) notations are confusing. Is it better to use L_i(x+1, y) = L_i(x, y) + dY_i = L_i(x, y) + A_i and L_i(x, y+1) = L_i(x, y) + dX_i = L_i(x, y) + B_i instead?
Is B_i supposed to be dX_i or -dX_i? The equation for L_i expands to dY_i * x - dY_i * X_i - dX_i * y + dX_i * Y_i, which means the coefficient for y is B_i = -dX_i. However, according to the equation for dL_i(x, y+1), dX_i = B_i. I think it needs to be changed to dL_i(x,y+1) = L_i(x,y) - dX_i.
It also interesting to see how this equation related to y = mx + b format.
Ax + By + C = 0 asserts that the point is on the edge aka on the line, so this form is equal to y =mx +b.
I believe this is a correct proof of equality:
Ax + By + C = 0
-By = Ax + C
y = -A/Bx - C/B, where m = -A/B and b = -C/B