2D Geometry

ハウスドルフ距離

# include <Siv3D.hpp>

void Main()
{
    Scene::SetBackground(ColorF(1.0, 0.96, 0.92));
    const Font font(40, Typeface::Heavy);

    const Polygon polygon = Shape2D::Star(240, Scene::Center());
    const LineString contour(polygon.outer());

    LineString contourClosed = contour;
    contourClosed << contour.front();

    // 精度を高めるため LineString を細かくする
    const LineString base = contourClosed.densified(10.0);

    LineString lines;
    double distance = Inf<double>;

    while (System::Update())
    {
        contour.drawClosed(12, ColorF(0.7));

        lines.draw(10, HSV(10, 1.0, 0.95));

        if (MouseL.pressed())
        {
            lines << Cursor::Pos();

            // ハウスドルフ距離を計算
            distance = Geometry2D::HausdorffDistance(base, lines);
        }

        if (MouseR.pressed())
        {
            lines.clear();
            distance = Inf<double>;
        }

        if (IsFinite(distance))
        {
            font(U"{:.2f}"_fmt(distance)).draw(20, 20, ColorF(0.25));
        }
    }
}

図形の重なる領域

# include <Siv3D.hpp>

void Main()
{
    const Polygon star = Shape2D::Star(200, Scene::Center());

    while (System::Update())
    {
        const Rect rect(Arg::center(Cursor::Pos()), 300, 100);

        star.drawFrame(2, Palette::Yellow);

        rect.draw(ColorF(1.0, 0.8));

        // star と rect の重なる領域を Polygon の配列で取得
        for (const auto& polygon : Geometry2D::And(star, rect.asPolygon()))
        {
            polygon.draw(ColorF(1.0, 0.0, 0.0, 0.5))
                .drawFrame(4, ColorF(1.0, 0.0, 0.0));
        }
    }
}

図形の引き算

# include <Siv3D.hpp>

void Main()
{
    const Polygon star = Shape2D::Star(200, Scene::Center());

    while (System::Update())
    {
        const Rect rect(Arg::center(Cursor::Pos()), 300, 100);

        star.drawFrame(2, Palette::Yellow);

        rect.drawFrame(2, ColorF(1.0, 0.8));

        // star から rect を引いた領域を Polygon の配列で取得
        for (const auto& polygon : Geometry2D::Subtract(star, rect.asPolygon()))
        {
            polygon.draw(ColorF(1.0, 0.0, 0.0, 0.5))
                .drawFrame(4, ColorF(1.0, 0.0, 0.0));
        }
    }
}

点群の凸包

# include <Siv3D.hpp>

void Main()
{
    Array<Vec2> points;

    Polygon convexHull;

    while (System::Update())
    {
        if (MouseL.down())
        {
            // 点を追加
            points << Cursor::Pos();

            // 凸包を計算
            convexHull = Geometry2D::ConvexHull(points);
        }

        convexHull.draw(Palette::Skyblue);

        for (const auto& point : points)
        {
            Circle(point, 5).draw(Palette::Seagreen);
        }
    }
}

Polygon の凸包

# include <Siv3D.hpp>

void Main()
{
    const Polygon star = Shape2D::Star(200, Scene::Center(), 15_deg);

    // 凸包を計算
    const Polygon convexHull = star.calculateConvexHull();

    while (System::Update())
    {
        convexHull.draw(Palette::Gray);

        star.draw(Palette::Yellow);
    }
}

Polygon の拡張

# include <Siv3D.hpp>

void Main()
{
    Polygon polygon;

    while (System::Update())
    {
        const Rect rect(Arg::center = Cursor::Pos(), 100);

        if (MouseL.down())
        {
            // polygon に rect を追加する
            // ただし、polygon と rect がつながらない場合は失敗して false を返す
            polygon.append(rect.asPolygon());
        }

        polygon
            .draw(Palette::Skyblue)
            .drawWireframe(1, Palette::White);

        rect.drawFrame(1, 0, Palette::Skyblue);
    }
}

Polygon の太らせ、細らせ

# include <Siv3D.hpp>

void Main()
{
    Scene::SetBackground(ColorF(0.6));

    const Polygon starBase1(Shape2D::Star(100, Scene::Center().movedBy(-160, 0)));
    const Polygon starBase2(Shape2D::Star(100, Scene::Center().movedBy(160, 0)));

    Polygon star1 = starBase1;
    Polygon star2 = starBase2;

    double distance = 0;

    while (System::Update())
    {
        if (SimpleGUI::Slider(U"{:.1f}"_fmt(distance), distance, -30.0, 30.0, Vec2(20, 20)))
        {
            // Polygon を太らせ / 細らせる
            star1 = starBase1.calculateRoundBuffer(distance);
            star2 = starBase2.calculateBuffer(distance);
        }

        star1.draw(Palette::Darkblue);
        star2.draw(Palette::Darkblue);

        starBase1.drawFrame(2, Palette::Yellow);
        starBase2.drawFrame(2, Palette::Yellow);
    }
}