mesh/src/trapezoidTriangulation.ts

import {
    addBoundingSquareTo,
    getDirectionSorter,
    Graph,
    GraphBoundary,
    GraphDirection,
    Point,
    Segment,
    SegmentWithIntersection, Triangle
} from "./pslg";

export function getFirstIntersectingSegmentInDirection(raySegment: Segment, boundary: GraphBoundary, graph: Graph, direction: GraphDirection): [Segment, Point] {
    const intersectingSegment = boundary.getBoundary(direction)
    const intersectingPoint = raySegment.getIntersectionWith(intersectingSegment)
    if ( !intersectingPoint ) {
        console.log(
            'getFirstIntersectingSegmentInDirection',
            [raySegment.from.coordinate, raySegment.to.coordinate],
            [intersectingSegment.from.coordinate, intersectingSegment.to.coordinate],
            intersectingPoint
        )
        throw new RangeError('Ray segment does not extend to boundary in the given direction!')
    }

    // Now, collect all non-boundary segments that intersect with the ray segment
    const intersections = (graph.segments
        .map(segment => {
            if ( boundary.isBoundarySegment(segment) ) return undefined

            return {
                segment,
                intersect: segment.getIntersectionWithin(raySegment)
            }
        })
        .filter(x => x && x.intersect) as SegmentWithIntersection[])
        .sort(getDirectionSorter(direction))

    const intersection = intersections[0]
    if ( intersection ) {
        return [intersection.segment, intersection.intersect]
    }

    return [intersectingSegment, intersectingPoint]
}

export function triangulate(originalGraph: Graph): Graph {
    const graph = originalGraph.clone()
    const boundary = addBoundingSquareTo(graph)

    const leftBound = boundary.getLeftBoundary()
    const rightBound = boundary.getRightBoundary()

    const trapezoidSegments: Segment[] = []

    // For each vertex in the original graph, create a horizontal line that
    // extends in both directions until it intersects with either (1) the boundary
    // or (2) a segment in the graph.
    for ( const point of graph.points ) {
        if ( boundary.isBoundaryPoint(point) ) continue  // skip boundary points

        // Create the segment extending out to the left boundary
        const leftPoint = Point.from(leftBound.from.x, point.y)
        let leftSegment = new Segment(point, leftPoint)

        // Get segments that intersect with this
        const leftIntersectingSegments = (graph.segments
            .map(segment => {
                if ( boundary.isBoundarySegment(segment) ) {
                    // Exclude boundary segments
                    return undefined
                }

                return {
                    segment,
                    intersect: segment.getIntersectionWithin(leftSegment),
                }
            })
            .filter(group => group && group.intersect) as Array<{segment: Segment, intersect: Point}>)
            .sort((a, b) => {
                return b.intersect.x - a.intersect.x  // Sort by right-most x-value
            })

        // Check if there was a nearer intersecting segment
        const firstLeftIntersectingSegment = leftIntersectingSegments?.[0]?.segment
        if ( firstLeftIntersectingSegment ) {
            // Modify the leftSegment to end at the intersection point
            const leftIntersect = graph.findExistingPointOrAdd(leftIntersectingSegments[0].intersect)
            leftSegment = new Segment(point, leftIntersect)
        }

        // Create the segment extending out to the right boundary
        const rightPoint = Point.from(rightBound.from.x, point.y)
        let rightSegment = new Segment(point, rightPoint)

        // Get segments that intersect with this
        const rightIntersectingSegments = (graph.segments
            .map(segment => {
                if ( boundary.isBoundarySegment(segment) ) {
                    // Exclude boundary segments
                    return undefined
                }

                return {
                    segment,
                    intersect: segment.getIntersectionWithin(rightSegment),
                }
            })
            .filter(group => group && group.intersect) as Array<{segment: Segment, intersect: Point}>)
            .sort((a, b) => {
                return a.intersect.x - b.intersect.x  // Sort by left-most x-value
            })

        // Check if there was a nearer intersecting segment
        const firstRightIntersectingSegment = rightIntersectingSegments?.[0]?.segment
        if ( firstRightIntersectingSegment ) {
            // Modify the leftSegment to end at the intersection point
            const rightIntersect = graph.findExistingPointOrAdd(rightIntersectingSegments[0].intersect)
            rightSegment = new Segment(point, rightIntersect)
        }

        const graphLeftSegment = graph.findExistingSegmentOrAdd(leftSegment)
        const graphRightSegment = graph.findExistingSegmentOrAdd(rightSegment)
        trapezoidSegments.push(graphLeftSegment, graphRightSegment)
    }

    // Now, go through and identify trapezoids for all the horizontal segments we just added
    for ( const segment of trapezoidSegments ) {
        // First, find the trapezoid formed with the segment as the bottom
        // Create a vertical segment from the midpoint of the segment to the top boundary
        const horizontalMidpoint = segment.getMidpoint()
        let upperBoundaryPoint = Point.from(horizontalMidpoint.x, boundary.ymax)
        let upperBoundaryVerticalSegment = new Segment(horizontalMidpoint, upperBoundaryPoint)

        const [upperIntersectSegment, upperIntersectPoint] = getFirstIntersectingSegmentInDirection(
            upperBoundaryVerticalSegment,
            boundary,
            graph,
            GraphDirection.UP
        )

        upperBoundaryVerticalSegment = new Segment(horizontalMidpoint, upperIntersectPoint)

        // Now we have the upper and lower boundaries of the trapezoid.
        // So, we need to figure out the left and right boundaries next.
        // Get the midpoint of the vertical segment
        const verticalMidpoint = upperBoundaryVerticalSegment.getMidpoint()
        let leftBoundaryPoint = Point.from(boundary.xmin, verticalMidpoint.y)
        let leftBoundaryHorizontalSegment = new Segment(verticalMidpoint, leftBoundaryPoint)

        const [leftIntersectSegment, leftIntersectPoint] = getFirstIntersectingSegmentInDirection(
            leftBoundaryHorizontalSegment,
            boundary,
            graph,
            GraphDirection.LEFT
        )

        leftBoundaryHorizontalSegment = new Segment(verticalMidpoint, leftIntersectPoint)

        // Repeat to get the right boundary
        let rightBoundaryPoint = Point.from(boundary.xmax, verticalMidpoint.y)
        let rightBoundaryHorizontalSegment = new Segment(verticalMidpoint, rightBoundaryPoint)

        const [rightIntersectSegment, rightIntersectPoint] = getFirstIntersectingSegmentInDirection(
            rightBoundaryHorizontalSegment,
            boundary,
            graph,
            GraphDirection.RIGHT,
        )

        rightBoundaryHorizontalSegment = new Segment(verticalMidpoint, rightIntersectPoint)

        // Now, check if we actually have a 4-bound trapezoid, or if we have a triangle
        const points = Point.distinct([
            segment.from,
            segment.to,
            upperIntersectSegment.from,
            upperIntersectSegment.to,
        ])

        if ( points.length === 3 ) {
            // We found a triangle! Less work.
            // Create the triangle and push it onto the graph
            const [p1, p2, p3] = points.map(x => graph.findExistingPointOrAdd(x))
            const s12 = graph.findExistingSegmentOrAdd(new Segment(p1, p2))
            const s23 = graph.findExistingSegmentOrAdd(new Segment(p2, p3))
            const s31 = graph.findExistingSegmentOrAdd(new Segment(p3, p1))
            graph.findExistingTriangleOrAdd(new Triangle([s12, s23, s31]))
            continue  // FIXME - remove to handle below-segment case
        }

        if ( points.length !== 4 ) {
            throw new RangeError('Found shape with invalid number of distinct points!')
        }

        // Now, we have the 4 bounding segments of the trapezoid.
        // Let's find the segments that make up the trapezoid
        // We will do this by re-creating segments for the four sides of the trapezoid
        // Split the left-side on the intersection point
        let [leftSegment1, leftSegment2] = leftIntersectSegment.splitAt(leftIntersectPoint)  // This is not right. Needs to be `segment`'s intersect point, not the midpoint intersect point
        graph.removeSegment(leftIntersectSegment)
        leftSegment1 = graph.findExistingSegmentOrAdd(leftSegment1)
        leftSegment2 = graph.findExistingSegmentOrAdd(leftSegment2)

        // We care about the upper-segment from the split, as that is the bound of our trapezoid
        const trapezoidLeftBoundSegment = leftSegment1.ymin === leftIntersectPoint.y ? leftSegment1 : leftSegment2

        // Repeat this process for the right-side segment
        let [rightSegment1, rightSegment2] = rightIntersectSegment.splitAt(rightIntersectPoint)
        graph.removeSegment(rightIntersectSegment)
        rightSegment1 = graph.findExistingSegmentOrAdd(rightSegment1)
        rightSegment2 = graph.findExistingSegmentOrAdd(rightSegment2)

        const trapezoidRightBoundSegment = rightSegment1.ymin === rightBoundaryPoint.y ? leftSegment1 : leftSegment2

        // Now we have all 4 bounding segments. We find the bisector that creates
        // triangles with the largest minimum angle.

        // First, try making triangles from bottom-left to top-right
        const lowerLeftPoint = graph.findExistingPointOrAdd(Point.from(segment.xmin, segment.ymin))
        const upperRightPoint = graph.findExistingPointOrAdd(Point.from(upperIntersectSegment.xmax, upperIntersectSegment.ymax))

        const bottomLeftBisectorSegment = new Segment(lowerLeftPoint, upperRightPoint)
        // const bottomLeftBisectorUpperTriangle = new Triangle([bottomLeftBisectorSegment, upperIntersectSegment, trapezoidLeftBoundSegment])
        // const bottomLeftBisectorLowerTriangle = new Triangle([bottomLeftBisectorSegment, segment, trapezoidRightBoundSegment])
        // const bottomLeftBisectorMinAngle = Math.min(bottomLeftBisectorUpperTriangle.getMinimumAngle(), bottomLeftBisectorLowerTriangle.getMinimumAngle())

        const upperLeftPoint = graph.findExistingPointOrAdd(Point.from(upperIntersectSegment.xmin, upperIntersectSegment.ymax))
        const lowerRightPoint = graph.findExistingPointOrAdd(Point.from(segment.xmax, segment.ymin))

        // const topRightBisectorSegment = new Segment(upperLeftPoint, lowerRightPoint)
        // const upperRightBisectorUpperTriangle = new Triangle([topRightBisectorSegment, upperIntersectSegment, trapezoidRightBoundSegment])
        // const upperRightBisectorLowerTriangle = new Triangle([topRightBisectorSegment, trapezoidLeftBoundSegment, segment])
        // const upperRightBisectorMinAngle = Math.min(upperRightBisectorUpperTriangle.getMinimumAngle(), upperRightBisectorLowerTriangle.getMinimumAngle())

        // const optimalBisectorUpperTriangle = upperRightBisectorMinAngle > bottomLeftBisectorMinAngle ? upperRightBisectorUpperTriangle : bottomLeftBisectorUpperTriangle
        // const optimalBisectorLowerTriangle = upperRightBisectorMinAngle > bottomLeftBisectorMinAngle ? upperRightBisectorLowerTriangle : bottomLeftBisectorLowerTriangle

        // Add the triangles to the graph
        // const upperTriangleSegments = optimalBisectorUpperTriangle.sides.map(side => graph.findExistingSegmentOrAdd(side))
        // graph.findExistingTriangleOrAdd(new Triangle(upperTriangleSegments as [Segment, Segment, Segment]))

        // const lowerTriangleSegments = optimalBisectorLowerTriangle.sides.map(side => graph.findExistingSegmentOrAdd(side))
        // graph.findExistingTriangleOrAdd(new Triangle(lowerTriangleSegments as [Segment, Segment, Segment]))
    }

    // FIXME handle the lower-trapezoid case

    return graph
}