Examples of UniformGridPattern

net.algart.math.patterns.UniformGridPattern
Interface, used by {@link Pattern} implementations to indicate thatthey are uniform-grid patterns, i.e. subsets of the set of all mesh nodes of some uniform grids. See also the section "Uniform-grid patterns" in the comments to {@link Pattern} interface.
More precisely, a pattern, implementing this interface, is some set of N points (N>0) x^(k) = (x₀^(k), x₁^(k), ..., x_n−1^(k)) (k=0,1,...,N−1, n= {@link #dimCount() dimCount()}), produced by the following formulas:
x₀^(k) = o₀ + i₀^(k)d₀
x₁^(k) = o₁ + i₁^(k)d₁
. . .
x_n−1^(k) = o_n−1 + i_n−1^(k)d_n−1

where o_j and d_j are some constants (d_j>0) and i_j^(k) are any integer numbers. The point o=(o₀,o₁,...,o_n−1), named origin of the grid, and the vector d=(d₀,d₁,...,d_n−1), named steps of the grid, are specified while creating the pattern. Moreover, these parameters about (o and d) are stored inside the object and can be quickly read at any time by {@link #originOfGrid()} and {@link #stepsOfGrid()} methods— this condition is a requirement for all implementations of this interface.

The numbers i_j^(k) are called grid indexes of the points of the pattern (or, briefly, grid indexes of the pattern). The integer points i^(k) = (i₀^(k), i₁^(k), ..., i_n−1^(k)) (k=0,1,...,N−1) form an integer pattern (see the section "Integer patterns" in the comments to {@link Pattern} interface),which is called grid index pattern and can be got at any time by {@link #gridIndexPattern()} method. If the number of points is not extremely large, the grid indexescan be also retrieved directly as Java set of i^(k) points by {@link #gridIndexes()} method.
Warning: not only patterns, implementing this interface, are actually such sets of points. Moreover, many patterns, created by this package, are really uniform grid (all their points really belong to set of mesh points of some uniform grid), but they do not implement this interface and are not considered to be "uniform-grid". The typical examples are Minkowski sums, created by {@link Patterns#newMinkowskiSum(Collection)} method,and unions, created by {@link Patterns#newUnion(Collection)} method.It is obvious that a Minkowski sum or a union of several uniform-grid patterns, having zero origin o=(0,0,...,0) and the same steps d, are also uniform-grid patterns with the same origin and steps. However, it is very probably that the objects, returned by {@link Patterns#newMinkowskiSum(Collection)} and {@link Patterns#newUnion(Collection)} methods,will not implement {@link UniformGridPattern} interface even in this "good" case.
Grid index restrictions

There are the following guarantees for grid indexes i_j^(k) of any uniform-grid pattern:
1. if p=(i₀,i₁,...,i_n−1) is the grid index of some point of the pattern, then − {@link #MAX_COORDINATE}≤i_j≤ {@link #MAX_COORDINATE}for all j;
2. if p=(i₀¹,i₁¹,...,i_n−1¹) and q=(i₀²,i₁²,...,i_n−1²) are the grid indexes of some two points of the pattern, then |i_j¹−i_j²|≤ {@link #MAX_COORDINATE} for all j.
Each implementation of this interface must fulfil both restriction. Any attempt to create a uniform-grid pattern, the grid indexes of which do not satisfy these restrictions, leads to {@link TooLargePatternCoordinatesException}.

These restrictions are guaranteed together with the coordinate restrictions, described in the section "Coordinate restrictions" in the comments to {@link Pattern} interface.These restrictions provide a guarantee that the method {@link #gridIndexPattern()} alwaysworks successfully and creates a correct integer pattern.

AlgART Laboratory 2007–2014
@author Daniel Alievsky @version 1.2 @since JDK 1.5

Examples of net.algart.math.patterns.UniformGridPattern

        for (int k = 0; k < ranges.length; k++) {
            ranges[k] = IRange.valueOf(Long.parseLong(args[++argIndex]), Long.parseLong(args[++argIndex]));
        }
        double step = Double.parseDouble(args[++argIndex]);
        int minimalPointCountForDecomposition = Integer.parseInt(args[++argIndex]);
        UniformGridPattern p = Patterns.newRectangularIntegerPattern(ranges)
            .multiply(step).shift(Point.valueOf(origin));
        System.out.println("Created pattern: " + p);
        System.out.println("Integer number of points: " + p.pointCount());
        System.out.println("Approximate number of points: " + p.largePointCount());
        if (p instanceof QuickPointCountPattern && ((QuickPointCountPattern) p).isPointCountVeryLarge()) {
            System.out.println("It is very large");
        }
        if (p.isActuallyRectangular()) {
            System.out.println("It is rectangular");
        }
        if (p.isSurelySinglePoint()) {
            System.out.println("It is 1-point");
        }
        if (p.isSurelyOriginPoint()) {
            System.out.println("It is origin of coordinates");
        }
        if (p.isSurelyInteger()) {
            System.out.println("It is integer");
        }
        if (p.pointCount() < 1000) {
            Pattern samePoints = Patterns.newPattern(p.points());
            System.out.println("Pattern with same points: " + samePoints);
            if (samePoints instanceof UniformGridPattern && ((UniformGridPattern)samePoints).isActuallyRectangular()) {
                System.out.println("It is also rectangular");
            }
        }
        System.out.println("Grid origin: " + p.originOfGrid());
        System.out.println("Grid steps vector: " + Point.valueOf(p.stepsOfGrid()));
        System.out.println("Minimal coordinates: " + p.coordMin());
        System.out.println("Maximal coordinates: " + p.coordMax());
        System.out.println("Minimal grid indexes: " + p.gridIndexMin());
        System.out.println("Maximal grid indexes: " + p.gridIndexMax());
        Set<IPoint> roundedPoints = p.roundedPoints();
        System.out.println(roundedPoints.size() + " rounded points");
        if (roundedPoints.size() < 1000) {
            System.out.println(new TreeSet<IPoint>(roundedPoints));
        }
        Set<Point> points = p.points();
        System.out.println(points.size() + " points");
        if (points.size() < 1000) {
            System.out.println(new TreeSet<Point>(points));
        }
        points = p.lowerSurface(0).points();
        System.out.println(points.size() + " left points:");
        if (points.size() < 1000) {
            System.out.println(new TreeSet<Point>(points));
        }
        points = p.upperSurface(0).points();
        System.out.println(points.size() + " right points:");
        if (points.size() < 1000) {
            System.out.println(new TreeSet<Point>(points));
        }
        points = p.surface().points();
        System.out.println(points.size() + " boundary:");
        if (points.size() < 1000) {
            System.out.println(new TreeSet<Point>(points));
        }
        System.out.println("Carcass:");
        System.out.println("    " + p.carcass() + " " + new TreeSet<Point>(p.carcass().points()));
        List<Pattern> unionDecomposition = p.unionDecomposition(minimalPointCountForDecomposition);
        System.out.println("Union decomposition to " + unionDecomposition.size() + " patterns:");
        for (Pattern q : unionDecomposition) {
            System.out.println("    " + q
                + (!q.hasMinkowskiDecomposition() ? " " + new TreeSet<Point>(q.points()) : ""));
        }
        List<Pattern> minkowskiDecomposition = p.minkowskiDecomposition(minimalPointCountForDecomposition);
        System.out.println("Minkowski decomposition to " + minkowskiDecomposition.size() + " patterns:");
        for (Pattern q : minkowskiDecomposition) {
            System.out.println("    " + q
                + (!q.hasMinkowskiDecomposition() ? " " + new TreeSet<Point>(q.points()) : ""));
        }

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Examples of net.algart.math.patterns.UniformGridPattern

        }
        long size = srcArray.length();
        long[] shifts = BasicMorphology.toShifts(null, size, dimensions, pattern, false);
        if (shifts.length == 0)
            throw new AssertionError("Empty pattern: it is impossible");
        UniformGridPattern roundedPattern = pattern.round();
        long[] leftShifts = BasicMorphology.toShifts(null, size, dimensions, roundedPattern.lowerSurface(0), false);
        long[] rightShifts = BasicMorphology.toShifts(null, size, dimensions, roundedPattern.upperSurface(0), false);
        if (leftShifts.length != rightShifts.length)
            throw new AssertionError("Unbalanced pattern.lowerSurface / pattern.upperSurface: different lengths");
        PArray processed = asProcessed(requiredType, srcArray, additionalArrays, dimensions,
            shifts, leftShifts, rightShifts);
        T result;

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Examples of UniformGridPattern

Grid index restrictions

Examples of net.algart.math.patterns.UniformGridPattern

Examples of net.algart.math.patterns.UniformGridPattern