How do I delete all the unnecessary white shapes, only keep the ones on the logo itself.

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If your texture is all vectors and you literally mean you want to delete all extra points outside your logo object... I'm a fan of this method:

  1. Start with 2 groups. A group with the texture and a group with the logo object.
  2. Duplicate the part of the logo object you want to apply the texture to...
    • Duplicate: Cmd + CCmd + F
    • This duplicate will essentially become the cookie cutter
  3. Object > Expand Appearance (If applicable)
  4. Object > Expand
  5. Window > Pathfinder flyout menu Make compound shape
  6. Window > PathfinderExpand (Progress image).
    • The original logo object is somewhere below the two visible groups.
  7. With the texture below the cookie cutter, select both and then do Window > PathfinderCrop ...and you get this.

You're left with 2 groups. The original logo object and a texture that is cut to the shape of the logo object.

You may also need to do steps 3 and 4 on the texture as well... Like if the texture is made with a brush for instance.


Using a Clipping Mask;

Create a circle until your edges and make sure it's on top of all other objects.

Select all and Right click → Make Clipping Mask

I've explained how clipping masks work in this answer.

You can also read more about clipping masks at Adobe.

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