Is there a formula or other means to find the matrix reflaction a line?
because it takes toooooooo long to find and I really hate! I think there is a formula, but do not know, I have found two formulas, but, but they do not always work …
I worked as a reflection of (x, y) on the line ax + by + C = 0 is the point x '= ((b ^ 2-a ^ 2) x-2aby – 2AC) / (a + b 2 ^ ^ 2) y' = ((a ^ 2-b ^ 2) and – 2abx – 2BC) / (a + b 2 ^ ^ 2) I did not check to see if it works, but is how I have it: the board of (x, y) (x ', y') must be perpendicular to the line. The slope line is a / b, and SO (y'-y) / (X 'x) = b / gives rise to an equation (1): bx – ay = bx – ay As the points are on opposite sides of the line, and the same distance, using the formula for the perpendicular distance from a point of a line (and ignoring the denominator, as the same for both points), get ax + 'from' + c = – (Ax + By + c) [Note: the minus sign because they are on opposite sides] therefore, we have the equation (2): ax + by '=- ax – by – 2c Solving these two equations for x and y' gives the formulas I have said before. A 2×2 matrix can be a reflection on a line through the origin or a rotation about the origin, but it implies a broader transformation and a translation can not make a right rotation of the array. On the other hand, if the reflection in a line through the origin, then c = 0, and the above equations can be represented by multiplying the left [x] [y] by the matrix [- (A ^ 2-b ^ 2) / (a ^ 2 + b ^ 2) ..... -2ab / (a + b 2 ^ ^ 2) ...] [-2ab / (a + b 2 ^ ^ 2) .............. (A ^ 2-b ^ 2) / a ^ 2 + b ^ 2]
Expressing a Projection on to a line as a Matrix Vector prod
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