// 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"
	"log"
	"math"
	"sort"

	"gonum.org/v1/gonum/stat"
)

type Triangulation struct {
	Points     []Vertex
	ConvexHull []Vertex
	Triangles  []int32
	Halfedges  []int32
}

// 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) ConcaveHull(quantile float64) []int32 {

	numTris := len(t.Triangles) / 3

	// Calculate the max edge lengths per triangle.
	lengths := make([]float64, numTris)
	for i := range lengths {
		idx := i * 3
		var max float64
		vs := t.Triangles[idx : idx+3]
		for j, vj := range vs {
			k := (j + 1) % 3
			if l := t.Points[vj].SquaredDistance2D(t.Points[vs[k]]); l > max {
				max = l
			}
		}
		lengths[i] = max
	}

	qs := make([]float64, len(lengths))
	copy(qs, lengths)
	sort.Float64s(qs)
	q := stat.Quantile(quantile, stat.LinInterp, qs, nil)
	log.Printf("info: %.2f%% quantile: %.2f\n", quantile, math.Sqrt(q))

	removed := map[int32]bool{}

	isBorder := func(n int32) bool {
		n *= 3
		for i := int32(0); i < 3; i++ {
			e := n + i
			if t.Halfedges[e] == -1 || removed[e] {
				return true
			}
		}
		return false
	}

	oldCandidates := make([]int32, 0, int(math.Ceil(float64(numTris)*(1.0-quantile))))
	log.Printf("info: cap candidates: %d\n", cap(oldCandidates))

	for i, length := range lengths {
		if length >= q {
			oldCandidates = append(oldCandidates, int32(i))
		}
	}

	var newCandidates []int32

	for len(oldCandidates) > 0 {
		log.Printf("candidates: %d\n", len(oldCandidates))

		oldRemoved := len(removed)

		for _, i := range oldCandidates {

			if isBorder(i) {
				removed[i] = true
			} else {
				newCandidates = append(newCandidates, i)
			}
		}

		if oldRemoved == len(removed) {
			break
		}

		oldCandidates = newCandidates
		newCandidates = newCandidates[:0]
	}

	log.Printf("info: triangles to remove: %d\n", len(removed))

	return nil
}

func (t *Triangulation) TriangleSlices() [][]int32 {
	sl := make([][]int32, len(t.Triangles)/3)
	var j int
	for i := range sl {
		sl[i] = t.Triangles[j : j+3]
		j += 3
	}
	return sl
}

func (t *Triangulation) Tin() *Tin {

	min := Vertex{math.MaxFloat64, math.MaxFloat64, math.MaxFloat64}
	max := Vertex{-math.MaxFloat64, -math.MaxFloat64, -math.MaxFloat64}

	vertices := t.Points

	for _, v := range vertices {
		min.Minimize(v)
		max.Maximize(v)
	}

	return &Tin{
		Vertices:  vertices,
		Triangles: t.TriangleSlices(),
		Min:       min,
		Max:       max,
	}
}

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] != int32(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
}