# How to move vertices of matrix in order to cast a 2d shadow?

I am trying to add shadows to my 2D xna game. Currently I have created a "shadow" using the texture of the caster with a transparent gray color, rotated, and stretched using a matrix. This, though, does not look like a real shadow, obviously. What I'm pretty sure I have to do is individually move the vertices of the matrix somehow in order to create a parallelogram so that the top and bottom sides are always parallel to the ground.

So, here are my questions:

1) Is this the correct way to cast shadows in a 2D game?

2) If so, how do I make a parallelogram out of the matrix? I've tried a vertex shader but that didn't go very well. I've also seen some people talk about using bones and using DynamicVertexBuffer, but I have no clue how to use them and can't find a tutorial on them.

3) If it isn't the correct way of casting shadows, then how should I do it? I don't want shadows like in Catalin's method, I want them to look like the shadow caster.

EDIT: I also just learned that the transformation I think I need to do is skew the matrix. XNA unfortunately does not include methods to do that, though.

EDIT 2: Here's a picture of the type of affine transformation I want to do (skewing): I have sort of solved the problem and in-case anyone else wants to know how to skew horizontally here is how:

Matrix skew = Matrix.Identity;
skew.M12 = (float)Math.Tan(Math.PI / 4); // replace Math.PI / 4 with the radian amount you want


I need to skew vertically (which I can do by rotating and rotating back, but is there a more efficient way?), though and would still like to know if this is the correct way of going about creating shadows in a 2D game, though

EDIT 3: Here's what I have done in my game, and this is how the shadows should look. I've used a bunch of math and transforming to achieve the matrix for the shadow. Hopefully I've done it the right way • You should probably post a picture that shows what you are trying to achieve. "Affine" is a category of transformations (including things like rotation, translation), whereas "skew" is a specific type of affine transformation. See this answer for a discussion of how to create a skew matrix. – Andrew Russell Oct 20 '14 at 15:14
• Thanks, I tried skewing using the method in the post but it won't work. I'm using Matrix s = Matrix.Identity; s.M12 = (float)Math.Tan(Math.PI / 2); EDIT: Yeah... I'm dumb. I was skewing it 180 degrees. Obviously it's going to dissapear. Thank you!! It works now – osum4est Oct 20 '14 at 15:22
• What's wrong with the Catalin's method? – Omar Oct 21 '14 at 12:43
• Catalins method creates no light behind the ahadow caster unless there is a light behind it, as if you were standing in a room with a light at waist level or so. What i want, though, is shadows that look like they are being created from the sun, like in real life. – osum4est Oct 21 '14 at 13:21
• If that's the problem you can simply overcome it by setting an ambient light and then by increasing the alpha of the shadows given by the Catalin's method. So you get a real nice effect. – Omar Oct 22 '14 at 20:40