private Tuple <Term, Term[]> TwoSilhouettesNoFeatures(TSnapped snappedPrimitive, ISet <FeatureCurve> annotated)
{
var sil0 = SegmentApproximator.ApproximateSegment(snappedPrimitive.LeftSilhouette.Points);
var sil1 = SegmentApproximator.ApproximateSegment(snappedPrimitive.RightSilhouette.Points);
var axis2d = Get2DVector(snappedPrimitive.AxisResult);
var sil0Top = GetForwardPoint(sil0, axis2d);
var sil0Bot = GetForwardPoint(sil0, -axis2d);
var sil1Top = GetForwardPoint(sil1, axis2d);
var sil1Bot = GetForwardPoint(sil1, -axis2d);
var topFit = ProjectionFit.Compute(
snappedPrimitive.TopFeatureCurve, new Point[] { sil0Top, sil1Top });
var botFit = ProjectionFit.Compute(
snappedPrimitive.BottomFeatureCurve, new Point[] { sil0Bot, sil1Bot });
if (annotated.Contains(snappedPrimitive.TopFeatureCurve))
{
topFit = Enumerable.Empty <Term>();
}
if (annotated.Contains(snappedPrimitive.BottomFeatureCurve))
{
botFit = Enumerable.Empty <Term>();
}
var objective = TermUtils.SafeSum(topFit.Concat(botFit));
var constraints = new Term[] { snappedPrimitive.Axis.NormSquared - 1 };
return(Tuple.Create(objective, constraints));
}
private static OptimizationProblem GetOptimizationProblem(IEnumerable <PrimitiveEditConstraint> constraints)
{
// generate constraint terms
var constraintTerms = new List <Term>();
var paramsToVars = new Dictionary <IEditParameter, ParameterVariable[]>();
foreach (var constraint in constraints)
{
TryAxisOnLine(constraintTerms, paramsToVars, constraint);
TryPointOnPlane(constraintTerms, paramsToVars, constraint);
}
// get variables
var variables =
(from vars in paramsToVars.Values
from var in vars
select var).ToArray();
// construct objective --> sum of squared distances to current values
var values = GetCurrentValues(variables);
var objective = TermUtils.SafeSum(
from i in Enumerable.Range(0, variables.Length)
select TermBuilder.Power(variables[i] - values[i], 2));
return(new OptimizationProblem
{
Constraints = constraintTerms.ToArray(),
Variables = variables,
Objective = objective,
});
}
private Tuple <Term, Term[]> TwoSilhouettesSingleFeature(TSnapped snappedPrimitive, ISet <FeatureCurve> annotated)
{
var sil0 = SegmentApproximator.ApproximateSegment(snappedPrimitive.LeftSilhouette.Points);
var sil1 = SegmentApproximator.ApproximateSegment(snappedPrimitive.RightSilhouette.Points);
var axis2d = Get2DVector(snappedPrimitive.AxisResult);
var isTopSnapped = snappedPrimitive.TopFeatureCurve.SnappedTo != null;
var isBottomSnapped = snappedPrimitive.BottomFeatureCurve.SnappedTo != null;
var snappedFeatureCurve = isTopSnapped ? snappedPrimitive.TopFeatureCurve : snappedPrimitive.BottomFeatureCurve;
var unsnappedFeatureCurve = isTopSnapped ? snappedPrimitive.BottomFeatureCurve : snappedPrimitive.TopFeatureCurve;
var sil0Top = GetForwardPoint(sil0, axis2d);
var sil0Bot = GetForwardPoint(sil0, -axis2d);
var sil1Top = GetForwardPoint(sil1, axis2d);
var sil1Bot = GetForwardPoint(sil1, -axis2d);
var sil0Far = isTopSnapped ? sil0Bot : sil0Top;
var sil1Far = isTopSnapped ? sil1Bot : sil1Top;
var featureProj = ProjectionFit.Compute(snappedFeatureCurve);
var farProj = Enumerable.Repeat(EndpointsProjectionFit(unsnappedFeatureCurve, sil0Far, sil1Far), 1);
var objective = TermUtils.SafeSum(new Term[] { TermUtils.SafeAvg(featureProj), TermUtils.SafeAvg(farProj) });
var constraints = new Term[] { snappedPrimitive.Axis.NormSquared - 1 };
return(Tuple.Create(objective, constraints));
}
private Term FeaturesTerm(IEnumerable <CircleFeatureCurve> iEnumerable)
{
var terms =
from item in iEnumerable
from term in ProjectionFit.Compute(item)
select term;
var objective = TermUtils.SafeAvg(terms);
return(objective);
}
private Tuple <Term, Term[]> FullInfo(TSnapped snappedPrimitive)
{
var terms =
from item in snappedPrimitive.FeatureCurves.Cast <CircleFeatureCurve>()
from term in ProjectionFit.Compute(item)
select term;
var objective = TermUtils.SafeAvg(terms);
var constraints = new Term[] { snappedPrimitive.Axis.NormSquared - 1 };
return(Tuple.Create(objective, constraints));
}
private static Term MeanSquaredError(Term[] terms, double[] values)
{
Contract.Requires(terms != null);
Contract.Requires(values != null);
Contract.Requires(terms.Length == values.Length);
Contract.Requires(Contract.ForAll(terms, term => term != null));
Contract.Ensures(Contract.Result <Term>() != null);
var errorTerms = from i in Enumerable.Range(0, terms.Length)
select TermBuilder.Power(terms[i] + (-values[i]), 2);
return((1 / (double)terms.Length) * TermUtils.SafeSum(errorTerms));
}
private static Tuple <Term, Term[]> CreateSGCTerms(SnappedStraightGenCylinder snappedPrimitive, double[] radii, Point spineStart, Point spineEnd)
{
var constraints = new Term[] { snappedPrimitive.Axis.NormSquared - 1 };
if (radii.Length > 0)
{
var featureCurveTerms =
from item in snappedPrimitive.FeatureCurves.Cast <CircleFeatureCurve>()
where item != null
where item.SnappedTo != null
from term in ProjectionFit.Compute(item)
select term;
var featureCurvesTerm = 0.1 * TermUtils.SafeAvg(featureCurveTerms);
// the difference between the primitive's radii and the computed radii is minimized
var radiiApproxTerm = TermUtils.SafeAvg(
from i in Enumerable.Range(0, snappedPrimitive.Components.Length)
let component = snappedPrimitive.Components[i]
let radius = radii[i]
select TermBuilder.Power(component.Radius - radius, 2));
// the smoothness of the primitive's radii (laplacian norm) is minimized
var radiiSmoothTerm = TermUtils.SafeAvg(
from pair in snappedPrimitive.Components.SeqTripples()
let r1 = pair.Item1.Radius
let r2 = pair.Item2.Radius
let r3 = pair.Item3.Radius
select TermBuilder.Power(r2 - 0.5 * (r1 + r3), 2)); // how far is r2 from the avg of r1 and r3
// we specifically wish to give higher weight to first and last radii, so we have
// an additional first/last radii term.
var endpointsRadiiTerm =
TermBuilder.Power(radii[0] - snappedPrimitive.Components.First().Radius, 2) +
TermBuilder.Power(radii.Last() - snappedPrimitive.Components.Last().Radius, 2);
// objective - weighed average of all terms
var objective =
radiiApproxTerm +
radiiSmoothTerm +
featureCurvesTerm +
endpointsRadiiTerm;
return(Tuple.Create(objective, constraints));
}
else
{
return(Tuple.Create((Term)0, constraints)); // if we can't extract radii approximation, we don't do any snapping
}
}
public static Term DiffSquared(TVec[] left, TVec[] right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Length == right.Length);
Contract.Requires(Contract.ForAll(left, item => item != null));
Contract.Requires(Contract.ForAll(right, item => item != null));
Contract.Requires(Contract.ForAll(0, left.Length, i => left[i].Dimension == right[i].Dimension));
var leftFlat = left.SelectMany(x => x.GetTerms()).ToArray();
var rightFlat = right.SelectMany(x => x.GetTerms()).ToArray();
return(TermUtils.DiffSquared(leftFlat, rightFlat));
}
/// <summary>
/// Parallelism measure of planes represented by three point triples.
/// </summary>
/// <param name="left">Three points to represent the first plane</param>
/// <param name="right">Three points to represent the second plane.</param>
/// <returns>A term measuring parallelism of the two planes.</returns>
public static Term PlaneParallelism3D(TVec[] left, TVec[] right)
{
Contract.Requires(left != null);
Contract.Requires(right != null);
Contract.Requires(left.Length == 3);
Contract.Requires(right.Length == 3);
Contract.Requires(Contract.ForAll(left, item => item != null));
Contract.Requires(Contract.ForAll(right, item => item != null));
Contract.Requires(Contract.ForAll(left, item => item.Dimension == 3));
Contract.Requires(Contract.ForAll(right, item => item.Dimension == 3));
var leftNormal = TermUtils.Normal3D(left[0], left[1], left[2]);
var rightNormal = TermUtils.Normal3D(right[0], right[1], right[2]);
return(VectorParallelism3D(leftNormal, rightNormal));
}
private Tuple <Term, Term[]> TwoSilhouettesSingleFeature(TSnapped snappedPrimitive, ISet <FeatureCurve> annotated)
{
var sil0 = SegmentApproximator.ApproximateSegment(snappedPrimitive.LeftSilhouette.Points);
var sil1 = SegmentApproximator.ApproximateSegment(snappedPrimitive.RightSilhouette.Points);
var snappedFeatureCurve = snappedPrimitive.TopCurve == null ? snappedPrimitive.BottomFeatureCurve : snappedPrimitive.TopFeatureCurve;
var unsnappedFeatureCurve = snappedPrimitive.TopCurve == null ? snappedPrimitive.TopFeatureCurve : snappedPrimitive.BottomFeatureCurve;
var sil0Far = GetFarPoint(sil0, snappedFeatureCurve.SnappedTo);
var sil1Far = GetFarPoint(sil1, snappedFeatureCurve.SnappedTo);
var featureProj = ProjectionFit(snappedFeatureCurve);
var farProj = ProjectionFit(unsnappedFeatureCurve, new Point[] { sil0Far, sil1Far });
if (annotated.Contains(unsnappedFeatureCurve))
{
farProj = Enumerable.Empty <Term>();
}
var objective = TermUtils.SafeSum(featureProj.Concat(farProj));
var constraints = new Term[] { snappedPrimitive.Axis.NormSquared - 1 };
return(Tuple.Create(objective, constraints));
}
private void OptimizeAll()
{
#region Write all variables and their current values to a vector
var variablesWriter = new VariableVectorsWriter();
var startVectorWriter = new VectorsWriter();
// write cylinders
foreach (var snappedCylinder in sessionData.SnappedPrimitives.OfType <SnappedCylinder>())
{
variablesWriter.Write(snappedCylinder);
startVectorWriter.Write(snappedCylinder);
}
// write cones
foreach (var snappedCone in sessionData.SnappedPrimitives.OfType <SnappedCone>())
{
variablesWriter.Write(snappedCone);
startVectorWriter.Write(snappedCone);
}
#endregion
// all objective functions. Will be summed eventually to form one big objective.
var objectives = new List <Term>();
// all equality constraints.
var constraints = new List <Term>();
var curvesToAnnotations = new Dictionary <FeatureCurve, ISet <Annotation> >();
#region Get mapping of curves to annotations
foreach (var fc in sessionData.FeatureCurves)
{
curvesToAnnotations[fc] = new HashSet <Annotation>();
}
foreach (var annotation in sessionData.Annotations)
{
IEnumerable <FeatureCurve> curves = null;
annotation.MatchClass <Parallelism>(pa => curves = pa.Elements);
annotation.MatchClass <Coplanarity>(ca => curves = ca.Elements);
annotation.MatchClass <Cocentrality>(ca => curves = ca.Elements);
Debug.Assert(curves != null);
foreach (var fc in curves)
{
curvesToAnnotations[fc].Add(annotation);
}
}
#endregion
#region get objectives and constraints for primitives
foreach (var snappedPrimitive in sessionData.SnappedPrimitives)
{
var objectiveAndConstraints = snappersManager.Reconstruct(snappedPrimitive, curvesToAnnotations);
objectives.Add(objectiveAndConstraints.Item1);
constraints.AddRange(objectiveAndConstraints.Item2);
}
#endregion
#region get constraints for annotations
foreach (var annotation in sessionData.Annotations)
{
var constraintTerms = GetAnnotationConstraints(annotation);
constraints.AddRange(constraintTerms);
}
#endregion
#region perform optimization
var finalObjective = TermUtils.SafeSum(objectives);
var vars = variablesWriter.ToArray();
var vals = startVectorWriter.ToArray();
var optimum = Optimizer.MinAugmentedLagrangian(finalObjective, constraints.ToArray(), vars, vals, mu: 10, tolerance: 1E-5);
#endregion
#region read data back from the optimized vector
var resultReader = new VectorsReader(optimum);
foreach (var snappedCylinder in sessionData.SnappedPrimitives.OfType <SnappedCylinder>())
{
resultReader.Read(snappedCylinder);
}
foreach (var snappedCone in sessionData.SnappedPrimitives.OfType <SnappedCone>())
{
resultReader.Read(snappedCone);
}
#endregion
#region Update feature curves
foreach (var snappedPrimitive in sessionData.SnappedPrimitives)
{
snappedPrimitive.UpdateFeatureCurves();
}
#endregion
}
private static Tuple <Term, Term[]> CreateBGCTerms(SnappedBendedGenCylinder snappedPrimitive, double[] radii, Point[] medial_axis)
{
var terms =
from item in snappedPrimitive.FeatureCurves.Cast <CircleFeatureCurve>()
where item.SnappedTo != null
from term in ProjectionFit.Compute(item)
select term;
var featureCurvesTerm = TermUtils.SafeAvg(terms);
var radiiApproxTerm = TermUtils.SafeAvg(
from i in Enumerable.Range(0, snappedPrimitive.Components.Length)
let component = snappedPrimitive.Components[i]
let radius = radii[i]
select TermBuilder.Power(component.Radius - radius, 2));
// the smoothness of the primitive's radii (laplacian norm) is minimized
var radiiSmoothTerm = TermUtils.SafeAvg(
from pair in snappedPrimitive.Components.SeqTripples()
let r1 = pair.Item1.Radius
let r2 = pair.Item2.Radius
let r3 = pair.Item3.Radius
select TermBuilder.Power(r2 - 0.5 * (r1 + r3), 2)); // how far is r2 from the avg of r1 and r3
var positionSmoothnessTerm = TermUtils.SafeAvg(
from triple in snappedPrimitive.Components.SeqTripples()
let p1 = new TVec(triple.Item1.vS, triple.Item1.vT)
let p2 = new TVec(triple.Item2.vS, triple.Item2.vT)
let p3 = new TVec(triple.Item3.vS, triple.Item3.vT)
let laplacian = p2 - 0.5 * (p1 + p3)
select laplacian.NormSquared);
Term[] TermArray = new Term[medial_axis.Length];
for (int i = 0; i < medial_axis.Length; i++)
{
TVec PointOnSpine = snappedPrimitive.BottomCenter + snappedPrimitive.Components[i].vS * snappedPrimitive.U + snappedPrimitive.Components[i].vT * snappedPrimitive.V;
TermArray[i] = TermBuilder.Power(PointOnSpine.X - medial_axis[i].X, 2) +
TermBuilder.Power(PointOnSpine.Y + medial_axis[i].Y, 2);
}
var spinePointTerm = TermUtils.SafeAvg(TermArray);
// we specifically wish to give higher weight to first and last radii, so we have
// an additional first/last radii term.
var endpointsRadiiTerm =
TermBuilder.Power(radii[0] - snappedPrimitive.Components.First().Radius, 2) +
TermBuilder.Power(radii.Last() - snappedPrimitive.Components.Last().Radius, 2);
// objective - weighed average of all terms
var objective =
0.1 * featureCurvesTerm +
radiiApproxTerm +
radiiSmoothTerm +
positionSmoothnessTerm +
spinePointTerm +
endpointsRadiiTerm;
var sB = snappedPrimitive.NPbot.X;
var tB = snappedPrimitive.NPbot.Y;
var s0 = snappedPrimitive.Components[0].vS;
var t0 = snappedPrimitive.Components[0].vT;
var s1 = snappedPrimitive.Components[1].vS;
var t1 = snappedPrimitive.Components[1].vT;
var botNormalParallelism = tB * (s1 - s0) - sB * (t1 - t0);
var sT = snappedPrimitive.NPtop.X;
var tT = snappedPrimitive.NPtop.Y;
var sLast = snappedPrimitive.Components[snappedPrimitive.Components.Length - 1].vS;
var tLast = snappedPrimitive.Components[snappedPrimitive.Components.Length - 1].vT;
var sBeforeLast = snappedPrimitive.Components[snappedPrimitive.Components.Length - 2].vS;
var tBeforeLast = snappedPrimitive.Components[snappedPrimitive.Components.Length - 2].vT;
var topNormalParallelism = tT * (sLast - sBeforeLast) - sT * (tLast - tBeforeLast);
var topNormalized = snappedPrimitive.NPtop.NormSquared - 1;
var botNormalized = snappedPrimitive.NPbot.NormSquared - 1;
var uNormalized = snappedPrimitive.U.NormSquared - 1;
var vNormalized = snappedPrimitive.V.NormSquared - 1;
var uvOrthogonal = TVec.InnerProduct(snappedPrimitive.U, snappedPrimitive.V);
var firstComponentBottomS = snappedPrimitive.Components[0].vS;
var firstComponentBottomT = snappedPrimitive.Components[0].vT;
var constraints = new List <Term>
{
topNormalized,
botNormalized,
uNormalized,
vNormalized,
uvOrthogonal,
firstComponentBottomS,
firstComponentBottomT,
botNormalParallelism,
topNormalParallelism
};
var meanRadius = radii.Sum() / radii.Length;
var stdDevRadius = Math.Sqrt(radii.Select(r => r * r).Sum() / radii.Length - meanRadius * meanRadius);
Debug.WriteLine("ALEXALEX Mean radius is {0}, stddev is {1}", meanRadius, stdDevRadius);
if (stdDevRadius <= 0.3 * meanRadius)
{
foreach (var pair in snappedPrimitive.Components.SeqPairs())
{
var ra = pair.Item1.Radius;
var rb = pair.Item2.Radius;
constraints.Add(ra - rb);
}
}
return(Tuple.Create(objective, constraints.ToArray()));
}
