In on-point settings the blocks are placed on the diagonal and triangles are added at the beginning and end of the rows to fill in so the quilt edge is straight and not zigzag. Then straight borders and binding may be added as desired.
Many traditional blocks are designed to be set on-point. They look better if set on-point. Examples of traditional on-point blocks are the basket block, cake stand block, or bride's bouquet. Other traditional blocks can be set in straight sets or set on-point. They look fine either way. But if blocks are set on-point rather than straight there is more diagonal movement evident making the quilt more interesting.
Many quilting books and online patterns include instructions for setting on-point. Some patterns even include cutting instructions for the side and corner triangles. If the cutting sizes are included you simply need to follow the instructions given. If they are not included you will need some simple formulas to calculate the sizes of squares to cut for cutting into triangles.
First make the blocks as instructed in your pattern. When all the blocks are finished you are ready to set them together. Next you will need to cut your setting triangles. There are acrylic tools available for purchase that will do the math for cutting the setting triangles. Check at your local quilt shop, discount fabric store, or online. Be very careful before you purchase a "setting tool" -- some of them are wonderful accurate tools, and with them you can cut your triangles to the exact size you need. The setting triangles will fit exactly with your blocks.
Other tools available for the same purpose will have you cut the triangles larger than necessary and then stitch them to the blocks and then trim. This method has some inaccuracy as you are cutting your triangles too large and sewing bias edges to your blocks. In sewing the bias edges to straight edges of blocks, it is inevitable that you will have some stretching of the bias edge when stitching. Then when you trim, your triangles may have a small variance of size and the edges might not be on the straight of the grain. Any inaccuracies at this point can make your borders not fit or become rippled as they are stitched on.
Remember before buying a "setting tool" be sure to carefully read the instructions so you will know if the triangles are cut accurately or cut larger and needing to be trimmed. Your choice depends on your quilting style. If you like to stitch and trim that is fine but many prefer to cut exactly the size needed first and then stitch.
If you don't wish to invest in a "setting tool" you may cut side triangles by first cutting large squares. Then slice on the diagonal twice yielding four triangles for each large square. The four corner triangles may be made by cutting two squares and then slice on the diagonal once. This way the bias edge will be stitched to the block and again the sides of the corners will be on the straight of grain.
To find size of square for side triangles
To find the size of square to cut for your side setting triangles -- use your inexpensive calculator and punch in numbers as follows -- 1.4142 (the square root of 2) x (times) the size of your finished quilt block. Now you know the diagonal of you quilt block. Add 1 1/4" to this number. That is the size of square you need to cut and slice diagonally twice to make the side triangles. For example your block is 12" finished -- 1.4142 x 12 = 16.97. Round up to the nearest 1/8 would be 17. 17 + 1.25 (1 1/4") = 18.25 or 18 1/4". So cut your squares 18 1/4" and slice them on the diagonal twice. This is for your side triangles. If you need twelve side triangles only cut three squares as each square makes four triangles.
Now some may wonder how to cut a square 18 1/4" when most of the acrylic square rulers are smaller than that measurement. I fold my fabric very carefully into fourths. Being careful to not cut on the two folded edges but to cut on the raw edges, I use a smaller square acrylic tool and cut a 9 1/8" square. Open it out and I have an 18 1/4" square. Another method that might not be as accurate is to use the grid measurement on your cutting mat. Trim two sides of the square and count over 18 1/4" and place your ruler and cut. Be sure to cut as accurately as you can. It is important to have everything fit together.
To cut the side setting triangles
The side triangles need to have the straight of the grain on the long edge making the long edge be the edge of the quilt that the borders are added to. To cut these triangles to get the grain line on the long edge, you will need to cut large squares and cut them on the diagonally twice using the following method. Place the squares on the cutting mat. Cut across the diagonal in one direction. Do not move the square. Place your ruler on the opposite diagonal and cut. You will have four triangles with the grain line on the long edge from each large square.
To find the size of square for corner triangles
The side triangles are half the finished size of the diagonal of the block + 7/8". For example 1.4142 x 12 = 16.97. Round up to 17 inches. One half of 17 is 8 1/2" + 7/8" = 9 3/8. You will cut your squares 9 3/8" and slice on the diagonal once. This will leave the bias edge on the long side of the triangle and the straight of the grain on the outside edges of the corner of the quilt.
To cut the corner setting triangles
Cut two corner squares the size calculated above. Place your ruler from corner to corner diagonally and cut once. Your two squares will yield four corner triangles.
First lay out your blocks on your design wall, bed or floor, with your side triangles and corner triangles placed at the edges and corners. Look at the diagonal row. Start in the top left corner. Right now ignore the top left corner triangle. Begin by stitching a side triangle to the first block, and another side triangle to the other side of the first block. Be careful to keep the side triangles and blocks in the proper orientation. You have now completed the first diagonal row. If you wish, you may now stitch the top left corner triangle to the top side of the first block.
Begin stitching row two. Begin with the side triangle and stitch to the first block. Stitch the second block to the first block and then the third block to the second block. Add a side triangle to the last block. Again remember to keep the orientation of the blocks and side triangles in the way you have laid them out.
As you stitch rows together you will notice that they are becoming longer. If your quilt is rectangular you will have two rows with the same number of blocks and triangles. Then your rows will begin to get shorter until you are stitching on the bottom right corner triangle.
Continue stitching rows as directed until all the rows are stitched together. I usually stitch all the rows first and then come back and stitch all the rows together. If you prefer to stitch each row to the previous row as you complete it that is OK too.
You will find that stitching rows of blocks on-point is no more difficult than stitching blocks in straight rows. The only difference is you are stitching your rows diagonally across the quilt and need to pay attention to the orientation of the side triangles and the blocks in order for everything to come out correctly.
Enjoy your lovely quilt with on-point setting.