/*
* Annotated scaffolding
*
*/
public static void FromPointsToLineSegment(LineSegmentSymbol lss)
{
var ls = lss.Shape as LineSegment;
Debug.Assert(ls != null);
var pt1Symbol = new PointSymbol(ls.Pt1);
var pt2Symbol = new PointSymbol(ls.Pt2);
string strategy;
TraceStep ts00 = new TraceStep(null, pt1Symbol, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(pt1Symbol));
TraceStep ts01 = new TraceStep(null, pt2Symbol, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(pt2Symbol));
TraceStep ts02 = null;
if (ls.Pt1.Concrete && ls.Pt2.Concrete)
{
ts02 = new TraceStep(null, lss, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(lss));
}
strategy = "Plot a Line Segment passing through two points.";
lss._innerLoop.Add(ts00);
lss._innerLoop.Add(ts01);
if (ts02 != null)
{
lss._innerLoop.Add(ts02);
}
lss.GenerateATrace(strategy);
/* string stepMetaRule = "Consider draw a line segment passing through the two points.";
* string stepAppliedRule = String.Format("Draw the line segment passing through two points {0} and {1}",
* pt1Symbol, pt2Symbol);
*
* var traceStep = new TraceStep(null, lss, stepMetaRule, stepAppliedRule);
* lss._innerLoop.Add(traceStep);*/
}
public static void FromPointsToMidPoint(PointSymbol ps1, PointSymbol ps2, PointSymbol midPoint)
{
//1. plot the ps1, ps2 and the line
//2. generate x coordinate
//3. generate y coordinate
//4. generate point (x,y)
string strategy;
var ts00 = new TraceStep(null, ps1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps1));
var ts01 = new TraceStep(null, ps2, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ps2));
var ls = LineBinaryRelation.Unify(ps1, ps2) as LineSymbol;
var ts02 = new TraceStep(null, ls, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ls));
strategy = "Plot the given two points and the connected line.";
midPoint._innerLoop.Add(ts00);
midPoint._innerLoop.Add(ts01);
midPoint._innerLoop.Add(ts02);
midPoint.GenerateATrace(strategy);
////////////////////////////////////////////////
var xCoord = new Var("x");
var pt1 = ps1.Shape as Point;
Debug.Assert(pt1 != null);
var pt2 = ps2.Shape as Point;
Debug.Assert(pt2 != null);
var term1 = new Term(Expression.Add, new List <object>()
{
pt1.XCoordinate, pt2.XCoordinate
});
var term2 = new Term(Expression.Divide, new List <object>()
{
term1, 2
});
var eq = new Equation(xCoord, term2);
/////////////////////////////////////////////////
object obj;
bool result = eq.IsEqGoal(out obj);
EqGoal goal1 = null;
if (result)
{
goal1 = obj as EqGoal;
Debug.Assert(goal1 != null);
Debug.Assert(goal1.Traces.Count == 1);
var currentTrace = goal1.Traces.ToList()[0];
strategy = "Generate x coordinate of midpoint.";
var newTrace = new Tuple <object, object>(strategy, currentTrace.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////
var yCoord = new Var("y");
term1 = new Term(Expression.Add, new List <object>()
{
pt1.YCoordinate, pt2.YCoordinate
});
term2 = new Term(Expression.Divide, new List <object>()
{
term1, 2
});
var eq1 = new Equation(yCoord, term2);
result = eq1.IsEqGoal(out obj);
EqGoal goal2 = null;
if (result)
{
goal2 = obj as EqGoal;
Debug.Assert(goal2 != null);
Debug.Assert(goal2.Traces.Count == 1);
var currentTrace1 = goal2.Traces.ToList()[0];
strategy = "Generate y coordinate of midpoint.";
var newTrace = new Tuple <object, object>(strategy, currentTrace1.Item2);
midPoint.Traces.Add(newTrace);
}
//////////////////////////////////////////////////////
var ps = new Point(xCoord, yCoord);
var psym = new PointSymbol(ps);
var mid = midPoint.Shape as Point;
Debug.Assert(mid != null);
var ps_inter1 = new Point(mid.XCoordinate, yCoord);
var psym_inter1 = new PointSymbol(ps_inter1);
var metaRule = "Consider substitute generate x coordinate into the point form.";
var appliedRule = SubstitutionRule.ApplySubstitute(goal1, psym);
var ts1 = new TraceStep(psym, psym_inter1, null, metaRule, appliedRule);
metaRule = "Consider substitute generate y coordinate into the point form.";
appliedRule = SubstitutionRule.ApplySubstitute(goal2, psym_inter1);
var ts2 = new TraceStep(psym_inter1, midPoint, null, metaRule, appliedRule);
strategy = "Generate point (x,y) by subsitute generated x and y.";
midPoint._innerLoop.Add(ts1);
midPoint._innerLoop.Add(ts2);
midPoint.GenerateATrace(strategy);
}
/*
* given m=2, k=3, y=3x+2
*/
public static void FromSlopeInterceptToLineSlopeIntercept(EqGoal slopeGoal, EqGoal interceptGoal, LineSymbol ls)
{
//1. Substitute slope and intercept properties into the line slope-intercept form y=mx+b.
////////////////////////////////////////////////////////
var ts0 = new TraceStep(null, slopeGoal, GeometryScaffold.KC_LineSlopeForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(slopeGoal));
var ts1 = new TraceStep(null, interceptGoal, GeometryScaffold.KC_LineInterceptForm, PlottingRule.PlottingStrategy, PlottingRule.Plot(interceptGoal));
ls._innerLoop.Add(ts0);
var abstractLs = new Line(ls.Shape.Label, slopeGoal.Lhs, interceptGoal.Lhs);
var abstractLss = new LineSymbol(abstractLs);
var internalLs = new Line(ls.Shape.Label, ls.SymSlope, interceptGoal.Lhs);
var internalLss = new LineSymbol(internalLs);
var traceStep1 = new TraceStep(abstractLss, internalLss, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(abstractLss, slopeGoal));
ls._innerLoop.Add(traceStep1);
ls._innerLoop.Add(ts1);
/*
* var rule = "Substitute given property to line slope-intercept form.";
* var appliedRule1 = string.Format("Substitute slope={0} into y=mx+b", ls.SymSlope);
* var appliedRule2= string.Format("Substitute intercept={0} into y=mx+b", ls.SymIntercept);*/
var traceStep2 = new TraceStep(internalLss, ls, SubstitutionRule.SubstituteKC(), SubstitutionRule.SubstitutionStrategy, SubstitutionRule.ApplySubstitute(internalLss, interceptGoal));
ls._innerLoop.Add(traceStep2);
string strategy = "Substitute slope and intercept properties into the line slope-intercept form y = mx + b.";
ls.GenerateATrace(strategy);
}
public static void LineSlopeIntercepToGraph(LineSymbol ls)
{
string strategy = strategy_graphing;
//Plotting shapes
//1. plotting Y-Intercept
//2. plotting X-Intercept
//3. plotting the line
//////////////////////////////////////////////////////////////
// Step 1:
var pt = new Point(0, ls.SymIntercept);
var ptSym = new PointSymbol(pt);
var ts0 = new TraceStep(null, ptSym, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym));
ls._innerLoop.Add(ts0);
//////////////////////////////////////////////////////////////
// Step 2:
var line = ls.Shape as Line;
Debug.Assert(line != null);
Equation eq;
if (line.B == null)
{
}
else
{
var x = new Var("x");
//step 2.1
var term = new Term(Expression.Multiply, new List <object>()
{
line.Slope, x
});
var term1 = new Term(Expression.Add, new List <object>()
{
term, line.Intercept
});
eq = new Equation(term1, 0);
object obj;
EqGoal gGoal = null;
bool result = eq.IsEqGoal(out obj);
if (result)
{
gGoal = obj as EqGoal;
}
if (gGoal != null)
{
double dX;
LogicSharp.IsDouble(gGoal.Rhs, out dX);
var pt1 = new Point(dX, 0);
var ptSym1 = new PointSymbol(pt1);
var ts1 = new TraceStep(null, ptSym1, null, PlottingRule.PlottingStrategy, PlottingRule.Plot(ptSym1));
ls._innerLoop.Add(ts1);
}
}
/////////////////////////////////////////////////////////////////
const string step1MetaRule = "Given the line slope-intercept form y=mx+b, plot the line by passing points (0,b) and (-b/m,0).";
string step1AppliedRule = String.Format("Plotting the line passing through (0,{0}) and ({1},0) ", ls.SymIntercept, ls.SymC);
//var ts = new TraceStep(null, ls.SlopeInterceptForm, step1MetaRule, step1AppliedRule);
string kc = GeometryScaffold.KC_LineGraphing;
var ts = new TraceStep(null, ls, kc, step1MetaRule, step1AppliedRule);
ls._innerLoop.Add(ts);
//////////////////////////////////////////////////////////////////
ls.GenerateATrace(strategy);
}
