Motion analysis: plots of a study's joint values and a point's path, and the parts that collide along it

- motion.plot: joint values and a point's path sampled as the study plays (closed loops
  following), with velocities and accelerations by finite differences, per step or per
  second with a duration.
- motion.interference: the pairs of parts that pass through each other along a study, with
  the first step, the step ranges, the depth and the shared volume; occurrences, against
  or contact sets choose the pairs; bounded samples and work.
- Motion Study dialog: a Study box opens a saved study; a chart of a joint value or a
  picked point with a cursor at the step shown (click to move there); Check collisions
  with the steps shaded on the chart. ui.start motion.study takes study.

crates/ui-egui/src/control.rs

@@ -371,11 +371,19 @@ fn dispatch(app: &mut SolveApp, ctx: &egui::Context, method: &str, p: &Value) ->
             let Some(id) = s("command") else { return err("missing `command`") };
             // `params`: what the dialog opens on. Refused: nothing starts, or the dialog closes.
             let params = p.get("params").filter(|v| !v.is_null());
-            if params.is_some() && id != "joint.drive" {
-                return err(format!("`{id}` takes no ui.start params yet (joint.drive takes joint, values)"));
+            if params.is_some() && id != "joint.drive" && id != "motion.study" {
+                return err(format!("`{id}` takes no ui.start params yet (joint.drive takes joint, values; motion.study takes study)"));
             }
             app.start(id);
-            if let Some(params) = params {
+            if let Some(params) = params.filter(|_| id == "motion.study") {
+                let Some(crate::dialogs::Kind::Motion(k)) = app.dialog.as_mut().map(|d| &mut d.kind) else {
+                    return err("Motion Study did not open");
+                };
+                if let Err(e) = crate::dialogs_motion::preset(&app.session, k, params) {
+                    crate::dialogs::cancel(app);
+                    return err(e);
+                }
+            } else if let Some(params) = params {
                 if app.tree.capture_prompt.is_some() {
                     return err("Drive Joints waits for the Capture Position question (ui.capture)");
                 }