diff --git a/.github/workflows/build_and_test.yml b/.github/workflows/build_and_test.yml
index c244123..9514767 100644
--- a/.github/workflows/build_and_test.yml
+++ b/.github/workflows/build_and_test.yml
@@ -20,9 +20,11 @@ jobs:
         sudo apt-get install -y build-essential cmake
 
     - name: build
+      working-directory: ${{ github.workspace }} 
       run: |
-        cmake -DCLOTH_DEBUG=ON .
+        cmake -DCLOTH_TESTING_ONLY=ON .
         make -j
 
     - name: test
+      working-directory: ${{ github.workspace }} 
       run: make test
diff --git a/.gitignore b/.gitignore
index d4fb281..8ea30e8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,7 +5,6 @@
 *.slo
 *.lo
 *.o
-*.obj
 
 # Precompiled Headers
 *.gch
diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..40242ff
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,46 @@
+# Copyright Matt Overby 2021.
+# Distributed under the MIT License.
+cmake_minimum_required(VERSION 3.5)
+
+project(cloth_sim_tutorial LANGUAGES CXX)
+
+option(CLOTH_DEBUG "run with debug options" OFF)
+option(CLOTH_TESTING_ONLY "only compile unit tests" OFF)
+
+set(CMAKE_CXX_STANDARD 14)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+list(PREPEND CMAKE_MODULE_PATH ${CMAKE_CURRENT_SOURCE_DIR}/cmake)
+add_definitions(-DCLOTH_ROOT_DIR="${CMAKE_CURRENT_SOURCE_DIR}")
+
+# Change compile flags for debug
+if (CLOTH_DEBUG)
+	add_definitions(-DCLOTH_DEBUG)
+	set(CMAKE_BUILD_TYPE Debug)
+	if(CMAKE_COMPILER_IS_GNUCC OR CMAKE_COMPILER_IS_GNUCXX)
+		set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall -Wundef -Wextra -Wno-long-long -Wlogical-op -Wshadow -Wmaybe-uninitialized")
+	endif()
+else()
+	set(CMAKE_BUILD_TYPE Release)
+endif()
+
+# Libigl also includes Eigen, etc
+include(libigl)
+
+# Gather src
+include_directories(${CMAKE_CURRENT_SOURCE_DIR}/src)
+file(GLOB SRC
+	${CMAKE_CURRENT_SOURCE_DIR}/src/*.hpp
+	${CMAKE_CURRENT_SOURCE_DIR}/src/*.cpp)
+
+# Create binary
+if (NOT CLOTH_TESTING_ONLY)
+	igl_include(glfw)
+	add_executable(${PROJECT_NAME} ${SRC})
+	target_link_libraries(${PROJECT_NAME} PUBLIC igl::glfw)
+endif()
+
+# Unit testing (work in progress)
+enable_testing()
+add_executable(cloth_test ${CMAKE_CURRENT_SOURCE_DIR}/test/test.cpp)
+target_link_libraries(cloth_test PUBLIC igl::core)
+add_test(NAME TestClothSolver COMMAND cloth_test)
diff --git a/README.md b/README.md
index 74e7534..465159a 100644
--- a/README.md
+++ b/README.md
@@ -1,2 +1,91 @@
-# optimization-cloth-tutorial
-A tutorial to implicit cloth simulation with numerical optimization 
+# Implicit Cloth Simulation with Gradient Descent
+
+A gentle introduction to optimization-based implicit time integration for [CSCI 5611](https://umtc.catalog.prod.coursedog.com/courses/8103481).
+
+_This is a work in progress. I released this around 2021 and it hasn't seen many updates. Please let me know if you have suggestions: mattoverby@gmail.com_
+
+## Introduction
+
+Cloth simulation is standard coursework for undergraduate computer graphics.
+Many assignments focus on explicit methods like [forward Euler](https://en.wikipedia.org/wiki/Euler_method).
+While efficient and simple, explicit integrators are notoriously unstable for large time steps and high stiffness.
+Implicit methods, e.g., [backward Euler](https://en.wikipedia.org/wiki/Backward_Euler_method), offer a solution to that problem.
+The standard [Baraff & Witkin approach](https://doi.org/10.1145/280814.280821) (B&W) forms a Taylor approximation to the Eqs. of motion, i.e., Newton's method.
+This results in a block-sparse linear system for which the velocity deltas are solved via [conjugate gradient](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf).
+
+The B&W method is conceptually straight forward. However, there are numerous gotchas not apparent in the original references.
+In particular, working out the Jacobians of some models can be nontrivial. Even when correct, the derivatives can still produce hard-to-debug instabilities.
+The [dynamic deformables course notes](https://doi.org/10.1145/3388769.3407490) describes this well, and I highly recommend reviewing the later chapters on cloth simulation for a thorough review of the topic.
+Nonetheless, implicit time integration remains a valuable and sometimes necessary tool for modern graphics applications.
+
+Recently, optimization-based methods have grown in popularity. This approach formulates the Eqs. of motion as an [iteratively minimized objective function](https://en.wikipedia.org/wiki/Optimization_problem).
+These methods provide unparalleled robustness and extensibility, e.g., [state of the art solvers](https://doi.org/10.1145/3450626.3459767) for cloth simulation.
+The implementation is often easier to construct piece-by-piece than B&W-style integrators.
+
+Below we describe a simple implicit solver for mass-spring systems using gradient descent.
+This is meant solely as a tutorial to optimization-based time stepping, and not for practical applications.
+For that, you'll want to consider higher-order optimization algorithms or [local-global type solvers](https://github.com/alecjacobson/computer-graphics-mass-spring-systems).
+
+## Implementation
+
+The objective we aim to minimize is the sum of internal elastic energy potentials plus a quadratic penalty of linear momentum:
+
+<img src="https://render.githubusercontent.com/render/math?math=\bar{x} = x %2B hv %2B h^2 M^{-1} f_{ext}">, <br/>
+<img src="https://render.githubusercontent.com/render/math?math=g(x) = \frac{1}{2h^2}\|M^{1/2}(x-\bar{x})\|^2 %2B \sum E(x)">,
+
+for vertex locations *x*, time step (sec) *h*, diagonal mass matrix *M*, velocities *v*, and external forces (gravity, wind, etc...)
+<img src="https://render.githubusercontent.com/render/math?math=f_{ext}">. The term <img src="https://render.githubusercontent.com/render/math?math=\bar{x}"> is the *explicit predictor*
+that is computed at the beginning of the time step. Computing a frame of animation amounts to iteratively minimizing the above objective until some convergence criteria is met
+(e.g., the norm of the gradient is below some threshold).
+
+### Interface
+
+Below we lay out the steps to produce an optimization-based solver for implicit cloth simulation.
+The dependencies will be fetched through a [DownloadProject](https://github.com/Crascit/DownloadProject) CMake script.
+[Eigen](https://eigen.tuxfamily.org) is used for linear algebra, which is an industry standard library for vector math.
+Rendering and mesh I/O is handled with [libigl](https://libigl.github.io) which also contains many excellent routines for mesh processing.
+In libigl, meshes are stored as two dense matrices, an nx3 matrix for vertices and an mx3 matrix for faces.
+Animating the mesh is done through a pre-draw callback in which we call our solver to update the vertex positions.
+It takes a little finesse to improve the rendering, so we'll save that for another day.
+
+To compile, execute the following commands:
+1. mkdir build
+2. cd build
+3. cmake ..
+4. make -j
+
+### Energies
+
+Whenever I write a new simulator, I start with the most basic elastic energy as the deformable primitives: a Hookean spring with stiffness *k* and rest length <img src="https://render.githubusercontent.com/render/math?math=\ell">. The potential energy of a spring is <img src="https://render.githubusercontent.com/render/math?math=(k/2)(\|x_a-x_b\|-\ell)^2">.
+These springs are created from the unique edges of tCe triangle mesh, with bending springs created between adjacent triangles.
+The [ClothMesh class](src/ClothMesh.hpp) generates this data given vertex and face buffers.
+We can also evaluate temporary springs to deal with collisions. One end point is the vertex, and the other is the projection onto the surface it's penetrating.
+
+### Optimization
+
+[Gradient descent](https://en.wikipedia.org/wiki/Gradient_descent) is a simple first-order method that steps along the negative gradient w.r.t. *x* at each iteration: <img src="https://render.githubusercontent.com/render/math?math=p = -\nabla g(x^i)">. We use *i* to denote the iteration and *p* as the descent direction. By all accounts, gradient descent is a poor choice due to its low rate of convergence. You can certainly improve performance with other higher-order optimizers. However, I personally advocate starting with gradient descent when writing new optimization code. The optimizer is so simple it's hard to make a mistake - if there are bugs, they are surely in your energy or gradient calculations. This can be a helpful debugging strategy!
+
+Each iteration, we have to make sure we aren't overshooting the objective and increase the energy. This is accomplished by scaling the descent direction with a scalar *s* using [line search](https://en.wikipedia.org/wiki/Line_search). All together, an iteration of gradient descent involves:
+
+<img src="https://render.githubusercontent.com/render/math?math=p = -\nabla g(x^i)">,<br>
+<img src="https://render.githubusercontent.com/render/math?math=s = linesearch(x^i, p)">,<br>
+<img src="https://render.githubusercontent.com/render/math?math=x^{i %2B 1} = x^i %2B s * p">.
+
+Both energy and gradient use similar calculations so you can save resources (and implementation efforts) by computing them both at same time. I like to use one function for both and skip gradient calculation with a conditional during line search. You can see the evaluation of the objective and gradient in the [Objective class](src/Objective.hpp), with gradient descent in [Solver](src/Solver.hpp).
+
+### Common Problems
+With these pieces you have enough to implement an implicit cloth solver. But there are a number of common problems to be aware of if your solver starts behaving erratically:
+- Using masses that aren't scaled by the area of the mesh
+- The cloth mesh is unrealistically large or small: Each unit of the implementation should correspond to one meter or centimeter. Whatever you choose, be consistent.
+- The time step is too large or small (it should be somewhere between 1/1000 and 1/20)
+- Forgetting to resize or initialize matrix values
+- Dividing by zero and error propogation: A single zero-length spring can produce instabilities, as its result is passed all the way up the food chain to the solver. Using asserts, guards, and std::isfinite any time you do a division will save you a lot of trouble (see the [Objective class](src/Objective.hpp) for an example).
+
+## Next Steps
+
+There are many ways to improve the solver illustrated above:
+- Parallelizing the objective and gradient calculation (I recommend [TBB](https://software.intel.com/en-us/oneapi/onetbb))
+- Collision against triangle meshes with a [signed distance field](https://github.com/InteractiveComputerGraphics/TriangleMeshDistance)
+- Better energy models with triangular elements ([Dynamic Deformables appendix D](https://doi.org/10.1145/3388769.3407490))
+- Preconditioning or accelerated versions of gradient descent
+- Optimizers with better convergence like [L-BFGS](https://en.wikipedia.org/wiki/Limited-memory_BFGS) or [projected Newton](https://doi.org/10.1145/1073368.1073394)
diff --git a/cmake/libigl.cmake b/cmake/libigl.cmake
new file mode 100644
index 0000000..1aae978
--- /dev/null
+++ b/cmake/libigl.cmake
@@ -0,0 +1,11 @@
+if(TARGET igl::core)
+    return()
+endif()
+
+include(FetchContent)
+FetchContent_Declare(
+    libigl
+    GIT_REPOSITORY https://github.com/libigl/libigl.git
+    GIT_TAG v2.5.0
+)
+FetchContent_MakeAvailable(libigl)
\ No newline at end of file
diff --git a/data/plane.obj b/data/plane.obj
new file mode 100644
index 0000000..a4f9c26
--- /dev/null
+++ b/data/plane.obj
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diff --git a/data/sphere.obj b/data/sphere.obj
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diff --git a/src/ClothAssert.hpp b/src/ClothAssert.hpp
new file mode 100644
index 0000000..7975731
--- /dev/null
+++ b/src/ClothAssert.hpp
@@ -0,0 +1,48 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#ifndef CLOTHASSERT_HPP
+#define CLOTHASSERT_HPP 1
+
+#include <cstdlib> 
+#include <string>
+#include <stdexcept>
+
+namespace cloth
+{
+
+static inline void AssertHandler(bool cond, const std::string& file, const int& line)
+{
+	if (!cond)
+	{
+		std::string err_msg = "Assertion failed in "+file+" line "+std::to_string(line);
+		throw std::runtime_error(err_msg.c_str());
+	}
+}
+
+static inline void AssertHandlerMsg(bool cond, const std::string& file, const int& line, const std::string &msg)
+{
+	if (!cond)
+	{
+		std::string err_msg = "Assertion failed in "+file+" line "+std::to_string(line)+": "+msg;
+		throw std::runtime_error(err_msg.c_str());
+	}
+}
+
+}
+
+// Neat trick that allows macros with multiple arguments:
+// https://stackoverflow.com/questions/3046889/optional-parameters-with-c-macros
+// Also consider using #condition
+
+#define ClothAssert_withmsg(cond, msg) AssertHandlerMsg(cond, std::string(__FILE__), __LINE__, msg)
+#define ClothAssert_nomsg(cond) AssertHandler(cond, std::string(__FILE__), __LINE__)
+#define ClothAssert_stripargs(xx,cond,msg,FUNC, ...) FUNC
+
+#define ClothAssert(...) \
+	ClothAssert_stripargs(,##__VA_ARGS__,\
+	ClothAssert_withmsg(__VA_ARGS__),\
+	ClothAssert_nomsg(__VA_ARGS__),\
+	)
+
+#endif
diff --git a/src/ClothMesh.hpp b/src/ClothMesh.hpp
new file mode 100644
index 0000000..214ab9d
--- /dev/null
+++ b/src/ClothMesh.hpp
@@ -0,0 +1,140 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#ifndef CLOTHMESH_HPP
+#define CLOTHMESH_HPP 1
+
+#include "ClothAssert.hpp"
+#include <Eigen/Dense>
+#include <map>
+
+namespace cloth
+{
+
+class ClothMesh
+{
+public:
+
+	Eigen::MatrixXd V; // rest vertices [nx3]
+	Eigen::MatrixXi F; // faces [fx3]
+	Eigen::MatrixXi E; // edges [ex3]
+	Eigen::VectorXd E0; // edge rest length
+	Eigen::MatrixXi B; // bend edges [bx3]
+	Eigen::VectorXd B0; // bend rest length
+	Eigen::VectorXd masses; // per-vertex masses
+	Eigen::VectorXi V_offset; // per-mesh index into V
+	Eigen::VectorXi F_offset; // per-mesh index into F
+
+	// Adds a mesh to the collection of deformables and returns mesh number
+	inline int add_mesh(const Eigen::MatrixXd &inV, const Eigen::MatrixXi &inF)
+	{
+		int mesh_idx = -1;
+		ClothAssert(inV.rows() > 0 && inV.cols()==3);
+		ClothAssert(inF.rows() > 0 && inF.cols()==3);
+
+		// First mesh?
+		if (V_offset.size()==0)
+		{
+			using namespace Eigen;
+			V_offset = VectorXi::Zero(2);
+			F_offset = VectorXi::Zero(2);
+			V_offset[1] = inV.rows();
+			F_offset[1] = inF.rows();
+			V = inV;
+			F = inF;
+			mesh_idx = 0;
+		}
+		else
+		{
+			mesh_idx = V_offset.size()-1;
+			V_offset.conservativeResize(mesh_idx+2);
+			F_offset.conservativeResize(mesh_idx+2);
+			V_offset[mesh_idx+1] = inV.rows();
+			F_offset[mesh_idx+1] = inF.rows();
+			V.conservativeResize(V.rows() + inV.rows(), 3);
+			V.bottomRows(inV.rows()) = inV;
+			F.conservativeResize(F.rows() + inF.rows(), 3);
+			F.bottomRows(inF.rows()) = inF;
+		}
+
+		masses = Eigen::VectorXd::Constant(V.rows(), 0.1/V.rows());
+
+		compute_edges();
+		return mesh_idx;
+	}
+
+	// Computes edges and cross-edges from faces
+	inline void compute_edges()
+	{
+		using namespace Eigen;
+		std::map<std::pair<int,int>, std::pair<int,int>> edges; // [edge, bend]
+		typedef std::map<std::pair<int,int>, std::pair<int,int>>::iterator EdgeIter;
+		int n_bend = 0; // keep track of valid bend edges (non-border)
+
+		int nf = F.rows();
+		for (int i=0; i<nf; ++i)
+		{
+			for (int j=0; j<3; ++j)
+			{
+				std::pair<int,int> edge = std::make_pair(F(i,j), F(i,(j+1)%3));
+				int adj = F(i,(j+2)%3);
+				if (edge.second < edge.first)
+				{
+					std::swap(edge.first, edge.second);
+				}
+
+				EdgeIter it = edges.find(edge);
+				if (it == edges.end())
+				{
+					edges[edge] = std::make_pair(adj, -1);
+				}
+				else
+				{
+					n_bend++;
+					std::pair<int,int> &adj_pair = it->second;
+					adj_pair.second = adj;
+					if (adj_pair.second < adj_pair.first)
+					{
+						std::swap(adj_pair.first, adj_pair.second);
+					}
+				}
+			}
+		}
+
+		// Loop over map and create eigen buffers
+		E = MatrixXi::Zero(edges.size(), 2);
+		E0 = VectorXd::Constant(edges.size(), -1);
+		B = MatrixXi::Zero(n_bend, 2);
+		B0 = VectorXd::Constant(n_bend, -1);
+
+		int edge_idx = 0;
+		int bend_idx = 0;
+		for(EdgeIter it = edges.begin(); it != edges.end(); ++it, ++edge_idx)
+		{
+			const std::pair<int,int> &e = it->first;
+			E(edge_idx,0) = e.first;
+			E(edge_idx,1) = e.second;
+			E0[edge_idx] = (V.row(e.first) - V.row(e.second)).norm();
+
+			const std::pair<int,int> &b = it->second;
+			if (b.first >= 0 && b.second >= 0)
+			{
+				ClothAssert(bend_idx < B.rows());
+				B(bend_idx,0) = b.first;
+				B(bend_idx,1) = b.second;
+				B0[bend_idx] = (V.row(b.first) - V.row(b.second)).norm();
+				bend_idx++;
+			}
+		}
+
+		// Check to make sure we set every edge
+		ClothAssert(E0.minCoeff() >= 0);
+		ClothAssert(B0.minCoeff() >= 0);
+
+	} // end compute edges
+
+};
+
+}
+
+#endif
diff --git a/src/Objective.hpp b/src/Objective.hpp
new file mode 100644
index 0000000..4e0d1ff
--- /dev/null
+++ b/src/Objective.hpp
@@ -0,0 +1,108 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#ifndef OBJECTIVE_HPP
+#define OBJECTIVE_HPP 1
+
+#include "ClothAssert.hpp"
+#include "ClothMesh.hpp"
+
+namespace cloth
+{
+
+class Objective
+{
+public:
+
+	// Computes and returns the Hookean energy of a spring with rest length r and stiffness k.
+	// If x.rows == grad.rows, the gradients (f, -f) are added to grad.
+	double spring_gradient(
+		const Eigen::MatrixXd &x,
+		int e0,
+		int e1,
+		double r,
+		double k,
+		Eigen::MatrixXd &grad) const
+	{
+		using namespace Eigen;
+		Vector3d x0 = x.row(e0);
+		Vector3d x1 = x.row(e1);
+		Vector3d edge = (x0-x1);
+		double l = edge.norm();
+		if (grad.rows() == x.rows() && l > 1e-12)
+		{
+			edge /= l;
+			edge *= (l-r)*k;
+			ClothAssert(edge.allFinite());
+			grad.row(e0) += edge;
+			grad.row(e1) -= edge;
+		}
+		double energy = 0.5 * k * (l-r) * (l-r); // (k/2)||l-l0||^2
+		ClothAssert(std::isfinite(energy));
+		return  energy;
+	}
+
+	// Spring energies that push vertices out of collision.
+	// We'll cheat a bit and hard code the sphere radius and center since we know it.
+	double collision_gradient(
+		const Eigen::MatrixXd &x,
+		int idx,
+		double k,
+		Eigen::MatrixXd &grad) const
+	{
+		using namespace Eigen;
+		Vector3d cent(0,0,0);
+		double rad = 0.51;
+		Vector3d xi = x.row(idx);
+		Vector3d dir = (xi-cent);
+		double l = dir.norm();
+		if (l > rad) { return 0; }
+		if (grad.rows() == x.rows() && l > 1e-12)
+		{
+			dir /= l;
+			dir *= (l-rad)*k;
+			ClothAssert(dir.allFinite());
+			grad.row(idx) += dir;
+		}
+		double energy = 0.5 * k * (l-rad) * (l-rad); // (k/2)||l-l0||^2
+		ClothAssert(std::isfinite(energy));
+		return energy;
+	}
+
+	// Momentum potential: ||x-xbar||^2_M / (2dt^2)
+	// Like springs above, if xrows == grad.rows, gradient is added.
+	// Unlike springs, the momentum is a global term.
+	inline double momentum_gradient(
+		const Eigen::MatrixXd &x,
+		const Eigen::MatrixXd &x_start,
+		const Eigen::MatrixXd &v,
+		const Eigen::VectorXd &masses,
+		double dt,
+		Eigen::MatrixXd &grad) const
+	{
+		using namespace Eigen;
+		// Some of this can be precomputed to speed up evaluations
+		MatrixXd x_bar = x_start + dt * v;
+		MatrixXd dx = x - x_bar;
+		MatrixXd M_dx = masses.asDiagonal() * dx;
+		double dot = 0;
+		for (int i=0; i<3; ++i)
+		{
+			dot += dx.col(i).dot(M_dx.col(i));
+		}
+
+		double energy = dot / (2.0*dt*dt);
+		if (grad.rows() == x.rows())
+		{
+			M_dx *= (1.0 / (dt*dt));
+			grad += M_dx;
+		}
+		ClothAssert(std::isfinite(energy));
+		return energy;
+	}
+
+};
+
+}
+
+#endif
diff --git a/src/Solver.hpp b/src/Solver.hpp
new file mode 100644
index 0000000..1b065a3
--- /dev/null
+++ b/src/Solver.hpp
@@ -0,0 +1,134 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#ifndef SOLVER_HPP
+#define SOLVER_HPP 1
+
+#include "Objective.hpp"
+#include "ClothMesh.hpp"
+
+namespace cloth
+{
+
+class Solver
+{
+public:
+
+	// State variables
+	Eigen::MatrixXd x; // positions [nx3]
+	Eigen::MatrixXd v; // velocities [nx3]
+	Eigen::MatrixXd x_start; // start of timestep [nx3]
+	double spring_k;
+	double bend_k;
+	double collision_k;
+	int max_solver_iter;
+
+	Solver() :
+		spring_k(100),
+		bend_k(100),
+		collision_k(300),
+		max_solver_iter(400)
+		{}
+
+	// Initalizes state variables, returns true if success
+	bool initialize(const ClothMesh &cloth)
+	{
+		if (cloth.V.rows() == 0 || cloth.V.cols() != 3)
+		{
+			return false;
+		}
+
+		x = cloth.V;
+		v = Eigen::MatrixXd::Zero(x.rows(), 3);
+		x_start = x;
+		return true;
+	}
+
+	// Computes the energy and gradient (if desired) of the objective
+	double gradient(const ClothMesh &cloth, const Objective &objective,
+		double dt, const Eigen::MatrixXd &xk, Eigen::MatrixXd &grad) const
+	{
+		double tot_energy = 0;
+
+		// Momentum potential
+		tot_energy += objective.momentum_gradient(
+			xk, x_start, v, cloth.masses, dt, grad);
+
+		// Stretch springs
+		int num_edges = cloth.E.rows();
+		for (int i=0; i<num_edges; ++i)
+		{
+			Eigen::RowVector2i e = cloth.E.row(i);
+			tot_energy += objective.spring_gradient(
+				xk, e[0], e[1], cloth.E0[i], spring_k, grad);
+		}
+
+		// Linear bend springs
+		int num_bend = cloth.B.rows();
+		for (int i=0; i<num_bend; ++i)
+		{
+			Eigen::RowVector2i b = cloth.B.row(i);
+			tot_energy += objective.spring_gradient(
+				xk, b[0], b[1], cloth.B0[i], bend_k, grad);
+		}
+
+		// Collision springs
+		int num_verts = xk.rows();
+		for (int i=0; i<num_verts; ++i)
+		{
+			tot_energy += objective.collision_gradient(
+				xk, i, collision_k, grad);
+		}
+
+		return tot_energy;
+	}
+
+	double energy(const ClothMesh &cloth, const Objective &objective, double dt, const Eigen::MatrixXd &xk) const
+	{
+		Eigen::MatrixXd dummy; // grad computation ignored if grad.size != x.size
+		return gradient(cloth, objective, dt, xk, dummy);
+	}
+
+	void solve(const ClothMesh &cloth, const Objective &objective, double dt)
+	{
+		using namespace Eigen;
+		ClothAssert(x.rows() == cloth.V.rows() && x.cols() == 3);
+		ClothAssert(v.rows() == x.rows() && v.cols() == x.cols());
+
+		x_start = x; // cache start state
+		v.col(1).array() += dt * -9.8; // gravity
+		x = x_start + dt * v; // initial guess
+		MatrixXd grad = MatrixXd::Zero(x.rows(), 3);
+		MatrixXd xk = MatrixXd::Zero(x.rows(), 3);
+
+		for (int iter = 0; iter < max_solver_iter; ++iter)
+		{
+			// Compute current energy and gradient
+			xk = x; // store state at current iteration
+			grad.setZero();
+			double energy_k = gradient(cloth, objective, dt, x, grad);
+
+			// Check for convergence
+			if (grad.norm() < 0.01)
+			{
+				break;
+			}
+
+			// Take a full step, i.e. alpha=1
+			x = xk - grad;
+
+			// Line search until objective decreased
+			double alpha = 1;
+			while (energy(cloth, objective, dt, x) > energy_k)
+			{
+				alpha *= 0.5;
+				x = xk - alpha * grad;
+			}
+		}
+	}
+
+};
+
+}
+
+#endif
diff --git a/src/main.cpp b/src/main.cpp
new file mode 100644
index 0000000..2b04ccd
--- /dev/null
+++ b/src/main.cpp
@@ -0,0 +1,82 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#include <igl/opengl/glfw/Viewer.h>
+#include <igl/readOBJ.h>
+#include <iostream>
+#include <Eigen/Geometry>
+#include "Solver.hpp"
+
+using namespace Eigen;
+using namespace cloth;
+
+int main(int argc, char *argv[])
+{
+	(void)(argc);
+	(void)(argv);
+
+	std::string plane = CLOTH_ROOT_DIR "/data/plane.obj";
+	std::string sphere = CLOTH_ROOT_DIR "/data/sphere.obj";
+	MatrixXd V, sphereV;
+	MatrixXi F, sphereF;
+	if (!igl::readOBJ(plane, V, F) || !igl::readOBJ(sphere, sphereV, sphereF))
+	{
+		return EXIT_FAILURE;
+	}
+
+	// Move cloth above the sphere
+	V.col(1).array() += 0.6;
+
+	// Create cloth object
+	ClothMesh cloth;
+	cloth.add_mesh(V, F);
+
+	// Objective function
+	Objective objective;
+
+	// Create solver
+	double dt = 1.0 / 24.0;
+	Solver solver;
+	if (!solver.initialize(cloth))
+	{
+		return EXIT_FAILURE;
+	}
+
+	std::cout << "Press A to simulate, R to reset" << std::endl;
+
+	// Create viewer
+	igl::opengl::glfw::Viewer viewer;
+	viewer.data().set_face_based(true);
+	viewer.data().set_mesh(V, F);
+	viewer.data().set_colors(RowVector3d(0.659, 0.847, 1));
+	viewer.append_mesh();
+	viewer.data(1).set_mesh(sphereV, sphereF);
+	viewer.data(1).set_colors(RowVector3d(0.7, 0.7, 0.7));
+	viewer.core().is_animating = false;
+
+	viewer.callback_key_pressed = [&](igl::opengl::glfw::Viewer&, unsigned int key, int)->bool
+	{
+		char c = char(key);
+		if (c == 'r')
+		{
+			solver.initialize(cloth);
+		}
+		return false;
+	};
+
+	viewer.callback_pre_draw = [&](igl::opengl::glfw::Viewer&)->bool
+	{
+		if (viewer.core().is_animating)
+		{
+			solver.solve(cloth, objective, dt); // solve the time step
+			V = solver.x; // update vertex positions
+			viewer.data(0).set_mesh(V, F);
+			viewer.data(0).compute_normals(); // update normals after defo
+		}
+		return false;
+	};
+
+	viewer.launch();
+
+	return EXIT_SUCCESS;
+}
diff --git a/test/test.cpp b/test/test.cpp
new file mode 100644
index 0000000..5a6bd9a
--- /dev/null
+++ b/test/test.cpp
@@ -0,0 +1,56 @@
+// Copyright Matt Overby 2021.
+// Distributed under the MIT License.
+
+#include <igl/readOBJ.h>
+#include <iostream>
+#include <Eigen/Geometry>
+#include "Solver.hpp"
+
+using namespace Eigen;
+using namespace cloth;
+
+int main(int argc, char *argv[])
+{
+	(void)(argc);
+	(void)(argv);
+
+	std::string plane = CLOTH_ROOT_DIR "/data/plane.obj";
+	std::string sphere = CLOTH_ROOT_DIR "/data/sphere.obj";
+	MatrixXd V, cV;
+	MatrixXi F, cF;
+	if (!igl::readOBJ(plane, V, F) || !igl::readOBJ(sphere, cV, cF))
+	{
+		return EXIT_FAILURE;
+	}
+
+	// Move cloth above the sphere
+	V.col(1).array() += 0.5;
+
+	// Create cloth object
+	ClothMesh cloth;
+	cloth.add_mesh(V, F);
+
+	// Objective function
+	Objective objective;
+
+	// Create solver
+	double dt = 1.0 / 24.0;
+	Solver solver;
+
+	// 20 iters won't converge but it will test
+	// all the functions are operational.
+	solver.max_solver_iter = 20;
+	
+	if (!solver.initialize(cloth))
+	{
+		return EXIT_FAILURE;
+	}
+
+    int timesteps = 10;
+    for (int step=0; step < timesteps; ++step)
+    {
+        solver.solve(cloth, objective, dt); // solve the time step
+    }
+
+	return EXIT_SUCCESS;
+}