This type of satin stich is used to cover a larger area of  pattern. This allows smaller and tighter satin stitches to be used instead of long and sagy ones. The pattern is broken up into smaller horizontal or vertical sections. Then, each section, at a time, is covered with satin stitch. The important thing to remember is that the satin stitch in the next row will always begin from between the two stitches from the previous row. This kind of stitch can be used wonderully with threads of different shades.

You need to know the satin stitch to be able to do this stitch. I will work on a leaf pattern.

encroaching_satin_stitch_1            encroaching_satin_stitch_2
Fig 1: I first divide the leaf pattern into sections. I have done 4 sections. This is to aid your stitching and also this tutorial. But, once you learn this stitch, making such sections is only a choice of convenience.   Fig 2: Bring the needle out from the edge of the first stitch line as in the illustration. Every stitch will be done straight. 
 encroaching_satin_stitch_3    encroaching_satin_stitch_4
Fig 3: Now, start doing the satin stitch to fill in the first section of the leaf. Such smaller satin stitches are more durable and good to look at.   Fig 4: Once you finish one section, it will look like this. Continue and bring the needle out from the second stitch line to fill the second section.
 encroaching_satin_stitch_5    encroaching_satin_stitch_6
Fig 5: You continue to fill up the next section with satin stitch as well. The only thing to be careful about is to set the stitches between two stitches of the previous section. See the illustration.   Fig 6: You continue the procedure of ‘encroaching’ between the stitches of the previous sections where they share the same stitch line. This is what gives the stitch its name.
 encroaching_satin_stitch_7   Fig 7: A finished pattern of leaf will look like this. If you click on the image, you will get a zoomed version where you can probably make out the ‘encroachments’. 🙂