mc-mesh/src/main/java/com/aaaaahhhhhhh/bananapuncher714/mesh/HalfEdge.java

package com.aaaaahhhhhhh.bananapuncher714.mesh;

/**
 * A half-edge class used to represent a DCEL(doubly connected edge list): https://en.wikipedia.org/wiki/Doubly_connected_edge_list
 * 
 * In this case, it is intended to be used for a 2d PSLG(planar straight-line graph), but can probably be repurposed
 * for some other nefarious use case.
 * 
 * An edge is a line segment connecting an origin to a destination. A half-edge is a partial line segment containing only
 * the origin, but not the destination.
 * 
 * Each half-edge structure contains:
 * - A reference to the origin
 * - A reference to the symmetrical, or opposite half-edge which is attached to the destination.
 * - A reference to the next clockwise half-edge of the opposite half edge. This can be used to
 *   traverse counter-clockwise through the half-edges of a polygon.
 * - A reference to the previous edge, which is the next counter-clockwise edge of this half edge.
 *   This can be used to traverse all the edges of a vertex, in counter clockwise order.
 * 
 * For a given half-edge attached to two points that contain no other edges, the previous edge is
 * itself, and the next edge is the same as the opposite edge.
 * 
 * There are 2 main operations that are used when manipulating half-edges to attach/detach them from
 * a vertex:
 * - splicing
 * - splitting
 * 
 * Splicing is the most important of the 2 operations, by a large margin. Given two half-edges, A and B,
 * swap the previous edges, and set the next edge for both of the previous edges to the opposite half edge.
 * This has the desired effect of either detaching two edges if they are connected to the same vertex, or
 * attaching two separate half-edges together to the same vertex.
 * 
 * Splitting is adding an edge between the opposite of an edge and attaching it to the destination. It
 * splits a single edge into two edges with a vertex in the middle.
 * 
 * @author BananaPuncher714
 */
public class HalfEdge {
    /**
     * The origin
     */
    protected Vertex origin;
    
    /**
     * The symmetrical half-edge
     */
    protected HalfEdge sym;
    /**
     * The half-edge counter-clockwise on the same origin
     */
    protected HalfEdge prev;
    /**
     * The half-edge clockwise from the symmetrical half-edge
     */
    protected HalfEdge next;
    
    // TODO Consider adding a constructor with a origin and destination
    
    public HalfEdge() {
        init();
        
        // Whenever we create a new half-edge, we need to make
        // sure that it has a symmetrical half-edge.
        new HalfEdge( this );
    }
    
    private HalfEdge( HalfEdge o ) {
        init();
        
        sym = o;
        o.sym = this;
        
        next = o;
        o.next = this;
    }
    
    private void init() {
        origin = new Vertex( this );
        prev = this;
    }
    
    public Vertex getOrigin() {
        return origin;
    }
    
    /**
     * Set the origin. Does not affect any additional 
     * 
     * @param vert
     * @return
     */
    public HalfEdge setOrigin( Vertex vert ) {
        origin = vert;
        return this;
    }
    
    public HalfEdge getSym() {
        return sym;
    }
    
    public HalfEdge getPrev() {
        return prev;
    }
    
    /**
     * Set the previous half-edge. Does not update additional properties.
     * 
     * @param edge The half-edge to set as the previous half-edge.
     * @return This half-edge
     */
    public HalfEdge setPrev( HalfEdge edge ) {
        this.prev = edge;
        return this;
    }
    
    public HalfEdge getNext() {
        return next;
    }
    
    /**
     * Set the next half-edge. Does not update additional properties.
     * 
     * @param edge The half-edge to set as the next half-edge.
     * @return This half-edge
     */
    public HalfEdge setNext( HalfEdge edge ) {
        this.next = edge;
        return this;
    }
    
    public Vertex getDest() {
        return sym.origin;
    }
    
    /**
     * Get the difference between the destination position and the origin position
     * 
     * @return A vector representing the destination minus the origin
     */
    public Vector2d toVector2d() {
        return getDest().getPosition().subtracted( getOrigin().getPosition() );
    }
    
    /**
     * Check if the origin and destination are the same
     * 
     * @return If the origin is equal to the destination
     */
    public boolean isZero() {
        return getOrigin().equals( getDest() );
    }
    
    /**
     * Split this half-edge in half and return the newly created
     * half-edge, as the next half-edge of this half-edge.
     * 
     * @return A new half-edge with a default initialized origin.
     */
    public HalfEdge split() {
        final HalfEdge edge = new HalfEdge();
        
        splice( edge, getNext() );
        
        splice( getSym(), getNext() );
        splice( getSym(), edge.getSym() );
        
        edge.setOrigin( getDest() );
        edge.getOrigin().setEdge( edge );
        
        getSym().setOrigin( edge.getDest() );
        getDest().setEdge( getSym() );
        
        edge.getOrigin().setEdge( edge );
        
        return edge.getSym();
    }
    
    /**
     * Splice two half-edges together. A commutative operation.
     * 
     * This does _not_ modify any vertices.
     * 
     * @param a The first half-edge
     * @param b The second half-edge
     */
    public static void splice( HalfEdge a, HalfEdge b ) {
        final HalfEdge ap = a.prev;
        final HalfEdge bp = b.prev;
        
        a.prev = bp;
        b.prev = ap;
        
        ap.sym.next = b;
        bp.sym.next = a;
    }
    
    @Override
    public String toString() {
        return String.format( "HalfEdge{orig=%1$s,dest=%2$s}", getOrigin(), getDest() );
    }
}