add a simple vector visualisation example

Signed-off-by: Michael Leuschel <leuschel@uni-duesseldorf.de>

Physics/VectorVisualisation.mch

+MACHINE VectorVisualisation
+// Small visualisation to show two vectors and various operations on them
+DEFINITIONS
+ NVECS==2;
+ VISB_JSON_FILE == "vector_visualisation_visb.json";
+ "LibrarySVG.def"
+INCLUDES Vectors2
+VARIABLES vectors
+INVARIANT
+  vectors : 1..NVECS --> VEC
+INITIALISATION vectors := [ [0.0, 2.0] , [2.0, 0.0] ]
+OPERATIONS
+  TimesVec(i,k) = PRE i:dom(vectors) & k: {0.5, 0.75, 1.5, 2.0} THEN
+    vectors(i) := times_vec(k,vectors(i))
+  END;
+  AddVec = BEGIN vectors(1):= add_vec(vectors(1),vectors(2)) END;
+  MakeUnit(i) = PRE i:dom(vectors) THEN vectors(i):= unit_vec(vectors(i)) END;
+  SwapXY(i) = PRE i:dom(vectors) THEN vectors(i):= rev(vectors(i)) END;
+  Opposite(i) = PRE i:dom(vectors) THEN vectors(i):= [-vectors(i)(1),-vectors(i)(2)] END
+END
+

Physics/vector_visualisation.svg

+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg
+   xmlns="http://www.w3.org/2000/svg"
+   height="500" width="500"
+   viewBox="-250 -250 500 500"
+   >
+
+
+   <defs>
+    <marker id="arrowhead" markerWidth="10" markerHeight="7"
+    refX="0" refY="3.5" orient="auto">
+      <polygon points="0 0, 10 3.5, 0 7" />
+    </marker>
+
+    <marker id="startarrow" markerWidth="10" markerHeight="7"
+    refX="10" refY="3.5" orient="auto">
+      <polygon points="10 0, 10 7, 0 3.5" fill="green" />
+    </marker>
+
+    <marker id="endarrow" markerWidth="10" markerHeight="7"
+    refX="0" refY="3.5" orient="auto">
+      <polygon points="0 0, 10 3.5, 0 7"  fill="green" />
+    </marker>
+  </defs>
+
+
+ <polyline points = "0 0, 100 100" id="axis" stroke="gray">
+
+</svg>

Physics/vector_visualisation_visb.json

+{
+  "svg": "vector_visualisation.svg",
+  "comment": "uses new svg object creation",
+  "definitions": [
+    { "name":"SCALE100",
+      "value" : "0.05"
+    }
+  ],
+  "svg_objects":[
+    {
+      "svg_class":"circle",
+      "id":"origin",
+      "cx":"0",
+      "cy":"0",
+      "r":"5",
+      "stroke-width":"0.0",
+      "fill":"green"
+    },
+    {
+      "for":{"from":1,"to":"NVECS"}, 
+      "svg_class":"line",
+      "id":"vector_%0",
+      "x1":"0",
+      "y1":"0",
+      "x2":"55",
+      "y2":"15",
+      "stroke":"#000",
+      "stroke-width":"1.75",
+      "marker-end":"url(#arrowhead)"
+    }
+  ],
+  "items": [
+    {
+      "id": "vector_1",
+      "attr": "stroke",
+      "value" : "\"blue\""
+    },
+    {
+      "id": "axis",
+      "attr": "points",
+      "value" : "svg_axis(0..10,1.0/SCALE100,10.0/SCALE100,0.2/SCALE100)"
+    },
+	{
+	  "for": {"from":1, "to":"NVECS"},
+      "id": "vector_%0",
+      "attr": "x2",
+      "value" : "vectors(%0)(1) / SCALE100"
+    },
+	{
+	  "for": {"from":1, "to":"NVECS"},
+      "id": "vector_%0",
+      "attr": "y2",
+      "value" : "-vectors(%0)(2)/ SCALE100"
+    }
+  ],
+  "events": [
+  ]
+}