Fix velocity update

README.md

@@ -1,8 +1,8 @@
 # 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).
+An 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_
+_This is a work in progress and was released around 2021. Please let me know if you have suggestions!_
 
 ## Introduction
 
@@ -20,7 +20,7 @@ Nonetheless, implicit time integration remains a valuable and sometimes necessar
 
 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.
+The implementation is often easier to construct piece-by-piece than B&W-style integrators. In this tutorial, you'll see why.
 
 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.
@@ -57,6 +57,8 @@ To compile, execute the following commands:
 3. cmake ..
 4. make -j
 
+Then press "A" to start the simulation.
+
 ### 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 $`\ell`$. The potential energy of a spring is $`(k/2)(\|x_a-x_b\|-\ell)^2`$.

src/Solver.hpp

@@ -116,6 +116,8 @@ class Solver
                 x = xk - alpha * grad;
             }
         }
+
+        v = (x - x_start) * (1.0 / dt);
     }
 };