diff --git a/Makefile b/Makefile
index e2a1064..c9a6c3f 100644
--- a/Makefile
+++ b/Makefile
@@ -1,5 +1,5 @@
 CXX= clang++-8
-CXXFLAGS= --std=c++17 -O0 -pthread -DGP_TESTS -DFUZZ_STRENGTH=500 -pedantic -Werror \
+CXXFLAGS= --std=c++17 -O3 -pthread -DGP_TESTS -DFUZZ_STRENGTH=500 -pedantic -Werror \
  -Wno-unknown-attributes \
  -g -fprofile-instr-generate -fcoverage-mapping
 # -fsanitize=address -fno-omit-frame-pointer
diff --git a/include/gp/math.hpp b/include/gp/math.hpp
index 93af11a..8a0910b 100644
--- a/include/gp/math.hpp
+++ b/include/gp/math.hpp
@@ -6,8 +6,14 @@
 #	include "gp/math/fp_math.hpp"
 #endif
 #include "gp/algorithm/repeat.hpp"
+#include "gp/algorithm/min_max.hpp"
 
 namespace gp {
+	template<typename T>
+	T lerp(T input, T low, T high) {
+		return low + (high - low) * input;
+	}
+
 	template<typename T, size_t fixed_passes = 16>
 	T fixed_sqrt(T value) {
 		if(value == 0) return 0;
@@ -101,6 +107,10 @@ namespace gp {
 			T ilen = fast_isqrt(x*x+y*y);
 			return {x*ilen, y*ilen};
 		}
+
+		T length() {
+			return fixed_sqrt(x*x+y*y);
+		}
 	};
 
 	template<typename T = gp_config::rendering::default_type>
@@ -175,6 +185,10 @@ namespace gp {
 			T ilen = fast_isqrt(x*x+y*y+z*z);
 			return {x*ilen, y*ilen, z*ilen};
 		}
+
+		T length() {
+			return fixed_sqrt(x*x+y*y+z*z);
+		}
 	};
 
 	template<typename T = gp_config::rendering::default_type>
@@ -260,8 +274,41 @@ namespace gp {
 			T ilen = fast_isqrt(x*x+y*y+z*z+w*w);
 			return {x*ilen, y*ilen, z*ilen, w*ilen};
 		}
+
+		T length() {
+			return fixed_sqrt(x*x+y*y+z*z+w*w);
+		}
 	};
 
+	template<typename T>
+	auto sphere_sdf(vec3_g<T> center, T radius) {
+		return [=](vec3_g<T> position) -> T const {
+			auto p = position - center;
+			return p.length() - radius;
+		};
+	}
+
+	template<typename T, typename lhs, typename rhs>
+	auto union_sdf(lhs _l, rhs _r) {
+		return [=](vec3_g<T> position) -> T const {
+			return gp::min(_l(position), _r(position));
+		};
+	}
+
+	template<typename T, typename lhs, typename rhs>
+	auto intersect_sdf(lhs _l, rhs _r) {
+		return [=](vec3_g<T> position) -> T const {
+			return gp::max(_l(position), _r(position));
+		};
+	}
+
+	template<typename T, typename lhs, typename rhs>
+	auto difference_sdf(lhs _l, rhs _r) {
+		return [=](vec3_g<T> position) -> T const {
+			return gp::max(_l(position), -_r(position));
+		};
+	}
+
 	template<typename T>
 	vec2_g<T> operator*(vec2_g<T> p, T v) {
 		return {p.x*v, p.y*v};
diff --git a/tests/math.cpp b/tests/math.cpp
index 7639ae3..048592f 100644
--- a/tests/math.cpp
+++ b/tests/math.cpp
@@ -46,14 +46,31 @@ struct render_test : public test_scaffold {
 		int res = 0;
 		renderer a;
 		a._resolution = vec2{128,64};
-		a.passes = 6;
-		a.projection_end = 4;
+		a.passes = 5;
+		a.projection_end = 3;
 
-		a.sky_box = [](vec3) -> color_t {return {0,0,0,0};};
-		auto v = a.materials.push(
+		a.sky_box = [](vec3) -> color_t {
+				color_t ret;
+				ret.r() = 0.5;
+				ret.g() = 0.5;
+				ret.b() = 1;
+				ret.a() = 1;
+				return ret;
+			};
+		auto red = a.materials.push(
 			[&](vec3 p) -> color_t {
 				color_t ret;
 				ret.r() = 1;
+				ret.g() = 0;
+				ret.b() = 0;
+				ret.a() = 1;
+				return ret;
+			}
+		);
+		auto green = a.materials.push(
+			[&](vec3 p) -> color_t {
+				color_t ret;
+				ret.r() = 0;
 				ret.g() = 1;
 				ret.b() = 0;
 				ret.a() = 1;
@@ -64,8 +81,22 @@ struct render_test : public test_scaffold {
 		auto sphere = a.scene_elements.push(
 			[=](vec3 pos) -> render_point {
 				render_point ret;
-				ret.distance = gp::fixed_sqrt<float, 6>(pos.x*pos.x + pos.y*pos.y  + pos.z*pos.z) - 1.0;
-				ret.material = v;
+				const auto l_sdf = gp::difference_sdf<float>(
+					gp::sphere_sdf<float>({0.0,0.0,0.0}, 1.0),
+					gp::sphere_sdf<float>({-0.75,0.0,0.0}, 1.0)
+				);
+				ret.distance = l_sdf(pos);
+				ret.material = red;
+				return ret;
+			}
+		);
+
+		auto sphere2 = a.scene_elements.push(
+			[=](vec3 pos) -> render_point {
+				render_point ret;
+				const auto l_sdf = gp::sphere_sdf<float>({-0.75,0.0,0.0}, 1.0);
+				ret.distance = l_sdf(pos);
+				ret.material = green;
 				return ret;
 			}
 		);