examples: improve the pendulum simulation, with several modes and diagrams (#13446)

examples/pendulum-simulation/modules/sim/sim.v

@@ -0,0 +1,47 @@
+module sim
+
+pub struct SimState {
+mut:
+	position Vector3D
+	velocity Vector3D
+	accel    Vector3D
+}
+
+pub fn new_state(state SimState) SimState {
+	return SimState{
+		...state
+	}
+}
+
+pub fn (mut state SimState) satisfy_rope_constraint(params SimParams) {
+	mut rope_vector := params.get_rope_vector(state)
+	rope_vector = rope_vector.scale(params.rope_length / rope_vector.norm())
+	state.position = vector(z: params.rope_length) + rope_vector
+}
+
+pub fn (mut state SimState) increment(delta_t f64, params SimParams) {
+	// 1. add up all forces
+	// 2. get an accelleration
+	// 3. add to velocity
+	// 4. ensure rope constraint is satisfied
+
+	// sum up all forces
+	forces_sum := params.get_forces_sum(state)
+
+	// get the acceleration
+	accel := forces_sum.scale(1.0 / params.bearing_mass)
+	state.accel = accel
+
+	// update the velocity
+	state.velocity = state.velocity + accel.scale(delta_t)
+
+	// update the position
+	state.position = state.position + state.velocity.scale(delta_t)
+
+	// ensure the position satisfies rope constraint
+	state.satisfy_rope_constraint(params)
+}
+
+pub fn (state SimState) done() bool {
+	return state.velocity.norm() < 0.05 && state.accel.norm() < 0.01
+}