diff --git a/src/r_main.c b/src/r_main.c
index 84d4630f0..a19d3fcf9 100644
--- a/src/r_main.c
+++ b/src/r_main.c
@@ -275,7 +275,7 @@ static void ChaseCam4_OnChange(void)
 //
 // killough 5/2/98: reformatted
 //
-INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *node)
+INT32 R_PointOnSideUDMF(fixed_t x, fixed_t y, const node_t *node)
 {
 	if (!node->dx)
 		return x <= node->x ? node->dy > 0 : node->dy < 0;
@@ -287,13 +287,31 @@ INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *node)
 	fixed_t dy = (y >> 1) - (node->y >> 1);
 
 	// Try to quickly decide by looking at sign bits.
-	if ((node->dy ^ node->dx ^ dx ^ dy) < 0)
-		return (node->dy ^ dx) < 0;  // (left is negative)
-	return FixedMul(dy, node->dx>>FRACBITS) >= FixedMul(node->dy>>FRACBITS, dx);
+	INT32 mask = (node->dy ^ node->dx ^ dx ^ dy) >> 31;
+	return (mask & ((node->dy ^ dx) < 0)) |  // (left is negative)
+		(~mask & (FixedMul(dy, node->dx>>FRACBITS) >= FixedMul(node->dy>>FRACBITS, dx)));
+}
+
+INT32 R_PointOnSideKart(fixed_t x, fixed_t y, const node_t *restrict node)
+{
+	if (!node->dx)
+		return x <= node->x ? node->dy > 0 : node->dy < 0;
+
+	if (!node->dy)
+		return y <= node->y ? node->dx < 0 : node->dx > 0;
+
+	x -= node->x;
+	y -= node->y;
+
+	// Try to quickly decide by looking at sign bits.
+	// also use a mask to avoid branch prediction
+	INT32 mask = (node->dy ^ node->dx ^ x ^ y) >> 31;
+	return (mask & ((node->dy ^ x) < 0)) |  // (left is negative)
+		(~mask & (FixedMul(y, node->dx>>FRACBITS) >= FixedMul(node->dy>>FRACBITS, x)));
 }
 
 // killough 5/2/98: reformatted
-INT32 R_PointOnSegSide(fixed_t x, fixed_t y, seg_t *line)
+INT32 R_PointOnSegSide(fixed_t x, fixed_t y, const seg_t *line)
 {
 	fixed_t lx = line->v1->x;
 	fixed_t ly = line->v1->y;
diff --git a/src/r_main.h b/src/r_main.h
index 6634c9b09..71d28af75 100644
--- a/src/r_main.h
+++ b/src/r_main.h
@@ -67,8 +67,10 @@ extern lighttable_t *zlight[LIGHTLEVELS][MAXLIGHTZ];
 #define NUMCOLORMAPS 32
 
 // Utility functions.
-INT32 R_PointOnSide(fixed_t x, fixed_t y, node_t *node);
-INT32 R_PointOnSegSide(fixed_t x, fixed_t y, seg_t *line);
+#define R_PointOnSide(x,y,node) udmf ? R_PointOnSideUDMF(x,y,node) : R_PointOnSideKart(x,y,node)
+INT32 R_PointOnSideUDMF(fixed_t x, fixed_t y, const node_t *node);
+INT32 R_PointOnSideKart(fixed_t x, fixed_t y, const node_t *node);
+INT32 R_PointOnSegSide(fixed_t x, fixed_t y, const seg_t *line);
 angle_t R_PointToAngle(fixed_t x, fixed_t y);
 angle_t R_PointToAnglePlayer(player_t *player, fixed_t x, fixed_t y);
 angle_t R_PointToAngle64(INT64 x, INT64 y);