Add Vector.copy(), +, and - to Mechanics.asy.

Also simplify Vector labeling to respect Label attributes (along the
lines of the earlier changes with LabeledCircle).

diff --git a/asymptote/Mechanics-test.asy b/asymptote/Mechanics-test.asy
index a99f0887eaa1c14a5c11d8109c38563649b8877f..9dc92ec6744deca20209f674779b53f3687c140b 100644 (file)
--- a/asymptote/Mechanics-test.asy
+++ b/asymptote/Mechanics-test.asy
@@ -62,7 +62,8 @@ vs.push(jhat(center=(0,u)));
 
 vs.push(Vector(center=(-1u,-4u), phi=90, "Out"));
 vs.push(Vector(center=(-1u,-5.5u), phi=-90, "In"));
-vs.push(Vector(center=(0, -4u), mag=1.5u, dir=-90, phi=60, "60dg OOP"));
+vs.push(Vector(center=(0, -4u), mag=1.5u, dir=-90, phi=60,
+               Label("60dg OOP", position=EndPoint)));
 
 for (int i=0; i<as.length; i+=1)
   as[i].draw();
@@ -87,6 +88,16 @@ p.draw(drawVertical=true);
 Surface s = Surface(pFrom=(0,-7u), pTo=(3.5u, -7u), L="Table");
 s.draw();
 
+Vector v1 = Vector((-2u, -7u), Label("$v_1$", align=E, position=EndPoint));
+v1.draw();
+Vector v2 = Vector(v1.center, mag=10mm, dir=90, Label("$v_2$", align=W));
+v2.draw();
+Vector v3 = v1 + v2;
+v3.label = Label("$v_3 = v_1 + v_2$", align=E, position=EndPoint);
+v3.draw();
+Vector v4 = v1 - v2;
+v4.label = Label("$v_4 = v_1 - v_2$", align=S, position=EndPoint);
+v4.draw();
 
 Vector v = Velocity();
 pair vfc = (5u,0);  // vector field center

diff --git a/asymptote/Mechanics.asy b/asymptote/Mechanics.asy
index 97e688929223e4974efa41b7f4d23e3abbdc835d..4c925fac8cd3600550d4ca15142cf47a84e4b134 100644 (file)
--- a/asymptote/Mechanics.asy
+++ b/asymptote/Mechanics.asy
@@ -123,7 +123,7 @@ struct Vector {
   real dir; // angle in the plane of the drawing.
   real phi; // angle with the plane of the drawing, 90 is out of the page.
   pen outline;
-  Label L;
+  Label label;
   real out_of_plane_radius;
   real out_of_plane_tolerance;
 
@@ -133,52 +133,77 @@ struct Vector {
     this.dir = dir;
     this.phi = phi;
     this.outline = outline;
-    this.L = L;
+    this.label = L;
     this.out_of_plane_radius = 1mm;
     this.out_of_plane_tolerance = 0.01;
   }
 
+  Vector copy() {
+    Vector v = Vector(center=this.center, mag=this.mag, dir=this.dir,
+                      phi=this.phi, outline=this.outline, L=this.label);
+    v.out_of_plane_radius = this.out_of_plane_radius;
+    v.out_of_plane_tolerance = this.out_of_plane_tolerance;
+    return v;
+  }
+
+  pair dTip() {  // offset from center to tip
+    pair p = (0,0);
+    real phi_e = this.phi % 360; // effective phi
+    if (Tan(phi_e) == 0 || abs(1.0/Tan(phi_e)) > this.out_of_plane_tolerance) {
+      return this.mag*Cos(this.phi)*dir(this.dir);
+    }
+    return (0, 0);
+  }
+
   pair pTip() {
-    return this.mag*dir(this.dir)+this.center;
+    return this.dTip() + this.center;
   }
-  
-  void draw(picture pic=currentpicture, bool rotateLabel=false, pair labelOffset=(0,0)) {
+
+  void draw(picture pic=currentpicture) {
     picture picF;
-    pair p = (0,0);
-    pair label_rotate = (1,0);
-    pair label_align = (0,1);
+    pair p = this.dTip();
+    path P;
     real phi_e = this.phi % 360; // effective phi
     if (this.mag < 0) (phi_e + 180) % 360;
     if (Tan(phi_e) == 0 || abs(1.0/Tan(phi_e)) > this.out_of_plane_tolerance) {
       // draw arrow in the plane of the drawing
       // TODO: thickening for phi?
-      p = this.mag*Cos(this.phi)*dir(this.dir);
-      path P = (0,0)--p;
+      P = (0,0)--p;
       draw(picF, P, outline, Arrow);
-      if (rotateLabel == true)
-        label_rotate = p;
-      label_align = unit(rotate(90)*p);
     } else if (phi_e > 0 && phi_e < 180) {
       // draw a circled dot for out-of-the-page
-      p = (0, this.out_of_plane_radius);
-      draw(picF, scale(this.out_of_plane_radius)*unitcircle, outline);
+      P = scale(this.out_of_plane_radius)*unitcircle;
+      draw(picF, P, outline);
       dot(picF, (0,0), outline);
     } else {
       // draw a circled cross for into-the-page
       real a = 0.8*sqrt(2.0)/2.0;
-      p = (0, this.out_of_plane_radius);
-      draw(picF, scale(this.out_of_plane_radius)*unitcircle, outline);
+      P = scale(this.out_of_plane_radius)*unitcircle;
+      draw(picF, P, outline);
       draw(picF, scale(this.out_of_plane_radius)*((-a,-a)--(a,a)), outline);
       draw(picF, scale(this.out_of_plane_radius)*((-a,a)--(a,-a)), outline);
     }
-    label(pic = picF,
-          L = rotate(degrees(label_rotate)) * L,
-          position = p+labelOffset,
-          align = label_align);
+    label(pic=picF, L=this.label, g=P);
     add(pic, picF, center);
   }
 }
 
+Vector operator +(Vector a, Vector b) {
+  Vector c = a.copy();
+  pair p = a.mag*dir(a.dir) + b.mag*dir(b.dir);
+  c.mag = length(p);
+  c.dir = degrees(p);
+  return c;
+}
+
+Vector operator -(Vector a, Vector b) {
+  Vector c = a.copy();
+  pair p = a.mag*dir(a.dir) - b.mag*dir(b.dir);
+  c.mag = length(p);
+  c.dir = degrees(p);
+  return c;
+}
+
 void vector_field(pair center=(0,0), real width=2cm, real height=2cm,
                   real dv=0.5cm, real buf=2pt, Vector v=null,
                   pen outline=invisible) {