Express Euclidean and Manhattan metric in terms of the Minkowski metric

1 files changed, 18 insertions, 8 deletions

diff --git a/example.cc b/example.cc
index a62fc48..18d0e78 100644
--- a/example.cc
+++ b/example.cc
@@ -3,14 +3,20 @@
 #include <cmath>
 #include <algorithm>
 
-double euclidean_metric(int refX, int refY, int x, int y) {
-	return std::sqrt(
-		std::pow(refX - x, 2) + std::pow(refY - y, 2)
+template <int p>
+double minkowski_metric(int refX, int refY, int x, int y) {
+	return std::pow(
+		std::pow(std::abs(refX - x), p) + std::pow(std::abs(refY - y), p),
+		1.0/p
 	);
 }
 
+double euclidean_metric(int refX, int refY, int x, int y) {
+	return minkowski_metric<2>(refX, refY, x, y);
+}
+
 int manhattan_metric(int refX, int refY, int x, int y) {
-	return std::abs(refX - x) + std::abs(refY - y);
+	return minkowski_metric<1>(refX, refY, x, y);
 }
 
 int main(int, char*[]) {
@@ -18,7 +24,7 @@ int main(int, char*[]) {
 
 	std::array<refpos, 5> ref{
 		refpos(100, 50,  imgen::color(255, 0,   0  )),
-		refpos(500, 300, imgen::color(0,   255, 0  )),
+		refpos(490, 300, imgen::color(0,   255, 0  )),
 		refpos(250, 250, imgen::color(0,   0,   255)),
 		refpos(400, 20,  imgen::color(100, 10,  100)),
 		refpos(60,  400, imgen::color(20,  60,  300))
@@ -33,12 +39,16 @@ int main(int, char*[]) {
 				ref.begin(),
 				ref.end(),
 				[x, y](const refpos& a, const refpos& b) -> bool {
-					return   manhattan_metric(std::get<0>(a), std::get<1>(a), x, y)
-					       < manhattan_metric(std::get<0>(b), std::get<1>(b), x, y);
+					return   minkowski_metric<5>(std::get<0>(a), std::get<1>(a), x, y)
+					       < minkowski_metric<5>(std::get<0>(b), std::get<1>(b), x, y);
 				}
 			);
 
-			return std::get<2>(nearest);
+			if ( euclidean_metric(std::get<0>(nearest), std::get<1>(nearest), x, y) <= 5 ) {
+				return imgen::color(0, 0, 0);
+			} else {
+				return std::get<2>(nearest);
+			}
 		}
 	);
 }