Step 3: Roll out the wrapping paper, and figure out the best layout to get the most liners from your paper.

Step 2: Place the paper in the envelope and make any changes to the template as needed. Step 4) Generate your envelope point list by doing a line intersect between all consecutive unique lines in results. Cut the paper just inside the tracing line, and just below the adhesive line.

Step 3) Repeat Step 2 until (?magic? measure of precision). Inserting into the results and culling inner repeats (line hits that have the same line on both sides). Step 2) Cast rays between consecutive hits of unique lines (1 and 2, and 3 and 4). Alternately, you can look through the solution and choose only intersections with increasing slope.Ĭonversely, any solution of this problem can be used to determine the upper convex hull of a set of points. Since you only want the upper envelope of your lines, you need to add a line lower than any possible regular line to eliminate the lower envelope. The dual of the convex hull gives you both the upper and lower envelope of the input line set. This is the envelope of the given set of lines. A customer recently asked us which adhesive is best to make your own professional-looking lined envelopes, free of lumps and bumps that many adhesives can leave behind. Correspondingly, the dual version of the convex hull determines those 'extreme' lines which are not convex combinations of others, as well as the points of intersection between successive extreme lines. To Line Your Envelopes You Need The Best Adhesive. Don’t worry if you find yourself doing this, because it takes years of patience to learn how to place one letter and word on the same level as the. In this case: the convex hull of a set of 2D points determines the 'extreme' points which are not convex combinations of others, as well as the lines between successive extreme points. How to write on your envelope in a straight line Even if your envelopes don’t cost 10 each, it’s still an incredible waste of paper and time if you write the address sloping down or up. This duality allows us to treat points as lines and lines as points: any proof or algorithm on points and lines can be mapped into an equally valid one with lines and points reversed. This inequality is also equivalent to the point (-a,b) being above the line (b)=x(-a)+y, where x is the slope and y is the intercept. Note: Conversely, any solution of this problem can also be used to build a 2D convex hull algorithm of the same O().įor a point (x,y) to be above a particular line y=ax+b, you have the inequality ax - y + b > 0. Solution: If you treat each line y=ax+b as a point (a,b), and add an additional 'point' at (0, -infinity), you should be able to feed this into any 2D convex hull algorithm and get a correct solution. A hint: this problem is basically a dual of the convex hull problem.

How to line envelopes