// Copyright (C) 2018 Michael Fogleman
//
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

package octree

import (
	"fmt"
	"math"
)

type Triangulation struct {
	Points     []Vertex
	ConvexHull []Vertex
	Triangles  []int
	Halfedges  []int
}

// Triangulate returns a Delaunay triangulation of the provided points.
func Triangulate(points []Vertex) (*Triangulation, error) {
	t := newTriangulator(points)
	err := t.triangulate()
	return &Triangulation{points, t.convexHull(), t.triangles, t.halfedges}, err
}

func (t *Triangulation) area() float64 {
	var result float64
	points := t.Points
	ts := t.Triangles
	for i := 0; i < len(ts); i += 3 {
		p0 := points[ts[i+0]]
		p1 := points[ts[i+1]]
		p2 := points[ts[i+2]]
		result += area(p0, p1, p2)
	}
	return result / 2
}

// Validate performs several sanity checks on the Triangulation to check for
// potential errors. Returns nil if no issues were found. You normally
// shouldn't need to call this function but it can be useful for debugging.
func (t *Triangulation) Validate() error {
	// verify halfedges
	for i1, i2 := range t.Halfedges {
		if i1 != -1 && t.Halfedges[i1] != i2 {
			return fmt.Errorf("invalid halfedge connection")
		}
		if i2 != -1 && t.Halfedges[i2] != i1 {
			return fmt.Errorf("invalid halfedge connection")
		}
	}

	// verify convex hull area vs sum of triangle areas
	hull1 := t.ConvexHull
	hull2 := ConvexHull(t.Points)
	area1 := polygonArea(hull1)
	area2 := polygonArea(hull2)
	area3 := t.area()
	if math.Abs(area1-area2) > 1e-9 || math.Abs(area1-area3) > 1e-9 {
		return fmt.Errorf("hull areas disagree: %f, %f, %f", area1, area2, area3)
	}

	// verify convex hull perimeter
	perimeter1 := polygonPerimeter(hull1)
	perimeter2 := polygonPerimeter(hull2)
	if math.Abs(perimeter1-perimeter2) > 1e-9 {
		return fmt.Errorf("hull perimeters disagree: %f, %f", perimeter1, perimeter2)
	}

	return nil
}