Defining an “inside room point” from wall points

问题

I need help with one tricky thing that I've tried to solve for a couple of days now. It feels like it should be relatively easy and that I am simply missing something somewhere.

I have an array defining each wall point (black dots) and I want to create a new inside point (green dots) for each wall point. The distance between each wall point and inside point should be 600.

I made a picture to show what I mean:

I'm writing this in javascript with aid of WebGL (ThreeJS).

回答1:

I'm going to propose a solution similar to David's, but using vertices rather than line segments. My solution also requires a consistent ordering of points, so I'll go with a clockwise ordering as well.

The following pseudocode will generate an ordered listing (in the same order as that of the original points) of new inside points:

d = 600    // distance of new inside point from wall point
for each 3 consecutive points (a, b, c)
   vector u = a - b; normalize u
   vector v = c - b; normalize v
   w = u + v; normalize w
   if angle (a, b, c) is convex    // cross product is positive: see below
      new inside point = b + (w * d) 
   else    // angle is concave/cross product is negative
      new inside point = b - (w * d)
   end
end

The cross product (u x v) is given by:

(x_u * y_v) - (y_u * x_v)

If the ordering is counter-clockwise, the signs of the cross product are reversed.

This does not check for collisions resulting from trying to put new inside points into a corridor of width less than 600, as @01zhou mentions in the comments.

回答2:

I don't have a code answer but this is how I would do it.

1. For the given point, get the two adjacent points and get their walls.
2. For each wall, draw a parallel line on either side of the wall.
3. Find the two lines that intersect. Wherever they intersect is the inside point that you're looking for.
4. If the three points share a common axis value (e.g. 3 points on the same line), then both sides will intersect. You will have to branch out to other points to discover which one to keep.

回答3:

First get a list of wall segments in (e.g.) clockwise order. Let's suppose that we have a wall segment from (a, b) to (c, d) going clockwise. The line defined by the segment is

(1 - t) (a, b) + t (c, d),

where t is variable. Inside is to the segment's right, where right is defined by the normal vector (d - b, a - c). Let

v = (d - b, a - c) / sqrt((d - b)**2 + (a - c)**2)

be the unit normal. Then, moved e units right, the new line is

(1 - t) (a, b) + t (c, d) + e v.

To determine the segments of the inner boundary, intersect each subsequent pair of lines defining the inner wall.

来源：https://stackoverflow.com/questions/23543212/defining-an-inside-room-point-from-wall-points