src/ClothesGraph.Geometry/Curves.cs - main - docNemo/clothes-graph

src/ClothesGraph.Geometry/Curves.cs
153 строки5 KB
docNemo
Фундамент продукта: параметрическое построение выкроек, печать, установщик
08 авг 2026, 22:17
08 авг 2026, 22:17cd47cce
using System;

namespace ClothesGraph.Geometry;

/// <summary>
/// Линия чертежа, параметризованная от 0 до 1.
/// </summary>
public interface ICurve
{
    Point2 Start { get; }
    Point2 End { get; }

    Point2 PointAt(double parameter);

    /// <summary>Длина линии.</summary>
    Length Length { get; }

    /// <summary>Точка на заданном расстоянии от начала вдоль линии.</summary>
    Point2 PointAtDistance(Length distance);

    /// <summary>Направление касательной в градусах против часовой стрелки.</summary>
    double DirectionAt(double parameter);
}

/// <summary>Прямолинейный отрезок.</summary>
public sealed class LineCurve(Point2 start, Point2 end) : ICurve
{
    public Point2 Start { get; } = start;
    public Point2 End { get; } = end;

    public Point2 PointAt(double parameter)
    {
        var offset = (End - Start) * Math.Clamp(parameter, 0, 1);
        return Start + offset;
    }

    public Length Length => Start.DistanceTo(End);

    public Point2 PointAtDistance(Length distance)
    {
        var total = Length;

        if (total.Units == 0)
            return Start;

        return PointAt(distance / total);
    }

    public double DirectionAt(double parameter) => (End - Start).Degrees;
}

/// <summary>
/// Кубическая кривая Безье.
/// </summary>
/// <remarks>
/// Длина считается разбиением на хорды: замкнутой формулы для длины кубической
/// кривой не существует, а точности разбиения хватает с большим запасом —
/// шаг разбиения даёт погрешность заметно ниже цены деления хранения.
/// </remarks>
public sealed class CubicCurve(Point2 start, Point2 control1, Point2 control2, Point2 end) : ICurve
{
    private const int LengthSamples = 128;

    public Point2 Start { get; } = start;
    public Point2 Control1 { get; } = control1;
    public Point2 Control2 { get; } = control2;
    public Point2 End { get; } = end;

    public Point2 PointAt(double parameter)
    {
        var t = Math.Clamp(parameter, 0, 1);
        var u = 1 - t;

        var x = u * u * u * Start.X.Units
                + 3 * u * u * t * Control1.X.Units
                + 3 * u * t * t * Control2.X.Units
                + t * t * t * End.X.Units;

        var y = u * u * u * Start.Y.Units
                + 3 * u * u * t * Control1.Y.Units
                + 3 * u * t * t * Control2.Y.Units
                + t * t * t * End.Y.Units;

        return new Point2(
            Length.FromUnits((long)Math.Round(x, MidpointRounding.AwayFromZero)),
            Length.FromUnits((long)Math.Round(y, MidpointRounding.AwayFromZero)));
    }

    public Length Length
    {
        get
        {
            var total = 0.0;
            var previous = Start;

            for (var index = 1; index <= LengthSamples; index++)
            {
                var current = PointAt(index / (double)LengthSamples);
                total += (current - previous).Magnitude.Units;
                previous = current;
            }

            return Length.FromUnits((long)Math.Round(total, MidpointRounding.AwayFromZero));
        }
    }

    public Point2 PointAtDistance(Length distance)
    {
        if (distance <= Length.Zero)
            return Start;

        var target = (double)distance.Units;
        var travelled = 0.0;
        var previous = Start;

        for (var index = 1; index <= LengthSamples; index++)
        {
            var parameter = index / (double)LengthSamples;
            var current = PointAt(parameter);
            var step = (current - previous).Magnitude.Units;

            if (travelled + step >= target)
            {
                var withinStep = step > 0 ? (target - travelled) / step : 0;
                var previousParameter = (index - 1) / (double)LengthSamples;

                return PointAt(previousParameter +
                               (parameter - previousParameter) * withinStep);
            }

            travelled += step;
            previous = current;
        }

        return End;
    }

    public double DirectionAt(double parameter)
    {
        var t = Math.Clamp(parameter, 0, 1);
        var u = 1 - t;

        var dx = 3 * u * u * (Control1.X.Units - Start.X.Units)
                 + 6 * u * t * (Control2.X.Units - Control1.X.Units)
                 + 3 * t * t * (End.X.Units - Control2.X.Units);

        var dy = 3 * u * u * (Control1.Y.Units - Start.Y.Units)
                 + 6 * u * t * (Control2.Y.Units - Control1.Y.Units)
                 + 3 * t * t * (End.Y.Units - Control2.Y.Units);

        return Math.Atan2(dy, dx) * 180.0 / Math.PI;
    }
}