gopatterns/pkg/pattern/path/splines.go

package path

import (
	"fmt"
	"git.wtrh.nl/patterns/gopatterns/pkg/pattern/point"
	"github.com/tdewolff/canvas"
	splines "gitlab.com/Achilleshiel/gosplines"
	"log/slog"
)

const resolution = 40

// Spline defines a smooth curved path through points.
type Spline struct {
	*Path
	start, end point.Point
}

type SplineOpts struct {
	Start, End point.Point
	Points     []point.Point
	Style      Style
}

// NewSpline returns a new spline through points. Start and end points can be provided as
// the start and stop direction of the spline. When start or end point arguments are left nil there
// are no constraints on the direction.
func NewSpline(opts SplineOpts) Spline {
	s := Spline{
		Path:  NewPath(opts.Points, opts.Style),
		start: opts.Start,
		end:   opts.End,
	}

	if opts.Start == nil && len(opts.Points) > 1 {
		s.start = opts.Points[0]
	}

	if opts.End == nil && len(opts.Points) > 1 {
		s.end = opts.Points[len(opts.Points)-1]
	}

	return s
}

// Draw the spline to the provided [canvas.Canvas].
func (s Spline) Draw(c *canvas.Canvas) error {
	points, err := s.build()
	if err != nil {
		return fmt.Errorf("generating spline: %w", err)
	}

	path := NewPath(points, s.style)

	if err = path.Draw(c); err != nil {
		return fmt.Errorf("draw spline points to canvas: %w", err)
	}

	length, _ := s.Length()
	slog.Debug("Draw spline", "length", length, "from", points[0].Name(), "to", points[len(points)-1].Name())

	return nil
}

func (s Spline) Length() (float64, error) {
	points, err := s.build()
	if err != nil {
		return 0.0, fmt.Errorf("generating spline: %w", err)
	}

	length := 0.0

	for i := range points[1:] {
		length += points[i].Position().Distance(points[i+1].Position())
	}

	return length, nil
}

func (s Spline) build() (points []point.Point, err error) {
	if len(s.points) < 2 {
		return s.points, nil
	}

	x := make([]float64, len(s.points))
	y := make([]float64, len(s.points))

	for i, p := range s.points {
		x[i], y[i] = p.Vector().Values()
	}

	diffStart := s.start.Vector().Subtract(s.points[0].Vector())
	diffEnd := s.points[len(s.points)-1].Vector().Subtract(s.end.Vector())

	xCoefficient, err := splines.SolveSplineWithConstraint(x, diffStart.X, diffEnd.X)
	if err != nil {
		return nil, fmt.Errorf("unable to calculate coefficients for x: %w", err)
	}

	yCoefficient, err := splines.SolveSplineWithConstraint(y, diffStart.Y, diffEnd.Y)
	if err != nil {
		return nil, fmt.Errorf("unable to calculate coefficients for y: %w", err)
	}

	points = make([]point.Point, 0, len(x)*resolution)
	stepSize := 1.0 / float64(resolution-1)

	for i := range len(s.points) - 1 {
		points = append(points, s.points[i])

		for t := stepSize; t < 1.0; t += stepSize {
			xCalculated := xCoefficient[i].Calculate(t)
			yCalculated := yCoefficient[i].Calculate(t)
			points = append(points, point.NewAbsolutePoint(xCalculated, yCalculated, 0, "0"))
		}
	}

	points = append(points, s.points[len(s.points)-1])

	return points, nil
}