Address PR feedback: speed-independent trail persistence with time-constant model

Replaces the draw-call-counter scope fade with a wall-clock-based
exponential decay. The user setting now means a literal trail
persistence in milliseconds, not an opaque alpha number.

Per @pfalstad on PR pfalstad#240:
- "vary alpha instead of the number of draw calls between fade outs"
- "should look the same regardless of the simulation speed setting"
- "It still seems too persistent even at the lowest setting"

Implementation:

  alpha = 1 - exp(-elapsed_ms / trailPersistence)

This is the analytic solution for an exponential decay with time
constant `trailPersistence`. Same fade rate at 30fps or 144fps,
because elapsed wall-clock time appears in the exponent. The user
sees and sets the time constant directly (default 200 ms).

Range 0..2000 ms. Setting trailPersistence = 0 maps to alpha = 1
(instant erase, no trail at all) so "lowest setting" really is no
trail, addressing the "still too persistent" complaint.

Persisted per-scope as XML attribute "tp"; omitted when at the
default to keep file size small.

The MOSFET lambda part of the original PR pfalstad#240 has been superseded
by PR pfalstad#313 (MosfetModel class), so this PR is now scope-fade-only.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: esaruoho

src/com/lushprojects/circuitjs1/client/Scope.java

@@ -262,6 +262,10 @@ class Scope {
     Canvas imageCanvas;
     Context2d imageContext;
     int alphaCounter =0;
+    // XY-plot trail persistence (wall-clock ms). 0 = instant erase (no trail).
+    int trailPersistence = 200;
+    static final int DEFAULT_TRAIL_PERSISTENCE = 200;
+    long lastTrailTime;
     // scopeTimeStep to check if sim timestep has changed from previous value when redrawing
     double scopeTimeStep;
     double scale[]; // Max value to scale the display to show - indexed for each value of UNITS - e.g. UNITS_V, UNITS_A etc.
@@ -1054,17 +1058,25 @@ void draw2d(Graphics g) {
     	g.context.translate(rect.x, rect.y);
     	g.clipRect(0, 0, rect.width, rect.height);
 
-    	alphaCounter++;
-    	
-    	if (alphaCounter>2) {
-    		// fade out plot
-    		alphaCounter=0;
-    		imageContext.setGlobalAlpha(0.01);
-    		if (app.isPrintable()) {
+    	// Wall-clock-based exponential fade. alpha = 1 - exp(-elapsed/persistence)
+    	// makes the trail look the same across simulation speeds: at 60fps a 200ms
+    	// persistence drops a pixel by 1-exp(-16/200) = 7.7% per frame; at 30fps
+    	// the same persistence drops by 1-exp(-33/200) = 15% per frame, so total
+    	// decay over a fixed wall-clock interval is constant.
+    	long now = System.currentTimeMillis();
+    	long elapsed = (lastTrailTime == 0) ? 16 : (now - lastTrailTime);
+    	lastTrailTime = now;
+    	double fadeAlpha;
+    	if (trailPersistence <= 0)
+    		fadeAlpha = 1.0; // instant erase = no trail
+    	else
+    		fadeAlpha = 1.0 - Math.exp(-elapsed / (double) trailPersistence);
+    	if (fadeAlpha > 0) {
+    		imageContext.setGlobalAlpha(fadeAlpha);
+    		if (app.isPrintable())
     			imageContext.setFillStyle("#ffffff");
-    		} else {
+    		else
     			imageContext.setFillStyle("#000000");
-    		}
     		imageContext.fillRect(0,0,rect.width,rect.height);
     		imageContext.setGlobalAlpha(1.0);
     	}
@@ -2211,6 +2223,8 @@ void dumpXml(Document doc, Element root) {
 
     	if (text != null)
 	    xmlElm.setAttribute("x", text);
+	if (trailPersistence != DEFAULT_TRAIL_PERSISTENCE)
+	    XMLSerializer.dumpAttr(xmlElm, "tp", trailPersistence);
     }
 
     void undumpXml(XMLDeserializer xml) {
@@ -2226,6 +2240,7 @@ void undumpXml(XMLDeserializer xml) {
 	position = xml.parseIntAttr("p", 0);
 	manDivisions = xml.parseIntAttr("md", 8);
 	text = xml.parseStringAttr("x", (String)null);
+	trailPersistence = xml.parseIntAttr("tp", DEFAULT_TRAIL_PERSISTENCE);
 	// Read trigger settings from parent <o> element before iterating children,
 	// because parseChildElement() changes the XML context to child <p> elements
 	int xmlTriggerMode = xml.parseIntAttr("triggerMode", TRIGGER_FREERUN);

src/com/lushprojects/circuitjs1/client/ScopePropertiesDialog.java

@@ -58,7 +58,8 @@ public class ScopePropertiesDialog extends Dialog implements ValueChangeHandler<
 CheckBox elmInfoBox;
 TextBox labelTextBox, manualScaleTextBox, divisionsTextBox;
 Button applyButton, scaleUpButton, scaleDownButton;
-Scrollbar speedBar,positionBar;
+Scrollbar speedBar, positionBar, trailBar;
+Label trailLabel;
 Scope scope;
 Grid grid, vScaleGrid, hScaleGrid;
 int nx, ny;
@@ -518,6 +519,20 @@ public void onClick(ClickEvent event) {
 		viBox.addValueChangeHandler(this); 
 		addItemToGrid(grid, xyBox = new ScopeCheckBox(Locale.LS("Plot X/Y"), "plotxy"));
 		xyBox.addValueChangeHandler(this);
+		Grid trailGrid = new Grid(1, 3);
+		trailGrid.setWidget(0, 0, new Label(Locale.LS("Trail Persistence (ms)")));
+		// Range 0..2000 ms; step 50; 0 = instant erase (no trail)
+		trailBar = new Scrollbar(Scrollbar.HORIZONTAL, scope.trailPersistence, 1, 0, 2050, new Command() {
+		    public void execute() {
+			scope.trailPersistence = trailBar.getValue();
+			setTrailLabel();
+		    }
+		});
+		trailGrid.setWidget(0, 1, trailBar);
+		trailLabel = new Label("");
+		trailGrid.setWidget(0, 2, trailLabel);
+		fp.add(trailGrid);
+		setTrailLabel();
 		if (transistor) {
 		    addItemToGrid(grid, vceIcBox = new ScopeCheckBox(Locale.LS("Show Vce vs Ic"), "showvcevsic"));
 		    vceIcBox.addValueChangeHandler(this);
@@ -625,7 +640,14 @@ void updateRowVisibility() {
 	void setScopeSpeedLabel() {
 	    scopeSpeedLabel.setText(CircuitElm.getUnitText(scope.calcGridStepX(), "s")+"/div");
 	}
-	
+
+	void setTrailLabel() {
+	    if (scope.trailPersistence <= 0)
+		trailLabel.setText(Locale.LS("none"));
+	    else
+		trailLabel.setText(scope.trailPersistence + " ms");
+	}
+
 	void addItemToGrid(Grid g, FocusWidget scb) {
 	    g.setWidget(ny, nx, scb);
 	    if (++nx >= grid.getColumnCount()) {