Consider placing three points, p1, p2, and p3 relative to each other, given the respective distances between points. Arbitrarily place p1 and p2 with respect to each other. There are then zero, one, or two solutions for p3. If there are two solutions for p3, maintain the original orientation of p3 with respect to the line p1 p2 oriented from p1 to p2.
The line is oriented, and the points, p1 and p2, are kept on the same side(s) of the line as they were in the original sketch. Furthermore, we preserve the orientation of the vector p1 p2 with respect to the line orientation by preserving the sign of the inner product with the line tangent vector. Thus in Figure 2, the correct solution is the filled point p2 on the right, rather than the open point p2(alt) on the left.
When placing a point relative to two lines, one of four possible locations is selected based on the quadrant of the oriented lines in which the point lies in the original sketch. Note that the line orientation permits an unambiguous specification of the angle between the lines.
There are two types of tangency possible between an arc and a segment. These two variations are shown in Figure 4. An arc tangent to two line segments will be centered such that the arc subtended preserves the type of tangency. Moreover, the center will be placed such that the smaller of the two arcs possible is chosen, ties broken by placing the center on the same side of the two segments as in the input sketch.