Signal Find

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Det[({{x_1, y_1, 1}, {x_2, y_2, 1}, {x_3, y_3, 1}})] = x_3 (y_1 - y_2) + x_1 (y_2 - y_3) + x_2 (y_3 - y_1)

Det[({{x_1, y_1, 1}, {x_2, y_2, 1}, {x_3, y_3, 1}})] <0 : Right

Det[({{x_1, y_1, 1}, {x_2, y_2, 1}, {x_3, y_3, 1}})] >0 : Left

{P_x, P_y}, {S_x, S_y}, {L_x, L_y}, {R_x, R_y}

P_x (S_y - R_y) + S_x (R_y - P_y) + R_x (P_y - S_y) >0

P_x (S_y - L_y) + S_x (L_y - P_y) + L_x (P_y - S_y) <0

P_y R_x - P_x R_y - P_y S_x + R_y S_x + P_x S_y - R_x S_y>0

-L_y P_x + L_x P_y + L_y S_x - P_y S_x - L_x S_y + P_x S_y<0

R_y (-P_x + S_x) + R_x (P_y - S_y) >P_y S_x - P_x S_y

L_y (-P_x + S_x) + L_x (P_y - S_y) <P_y S_x - P_x S_y

L_y (-P_x + S_x) + L_x (P_y - S_y) <P_y S_x - P_x S_y<R_y (-P_x + S_x) + R_x (P_y - S_y)

(L_x - R_x) (P_y - S_y) < (L_y - R_y) (P_x - S_x)

(P_y - S_y)/(P_x - S_x) < (L_y - R_y)/(L_x - R_x)