In Times Square, NYC, a large screen wraps around a building. In late 2024, a perfume bottle would dance inside the screen and then pop out of it. In the National Gallery in London, there is a distorted painting of a Dutch interior across the inside of a box. When viewed through a peephole, one sees a distortion-free 3D image of the interior. We have designed an origami piece that has distorted silhouettes and a pattern of triangles and distorted rectangles. When folded and viewed from the correct vantage point an illusion of a chessboard on the floor of a cube and silhouettes on the faces emerges. All three of the objects draw on a specific application of projective geometry. A second application is an animation that draws an ice skater that then moves around within the 3D space of a photograph. In this paper, we will reveal how the math works and use vector algebra as an alternative to traditional tools like a ruler and compass, a projector, or specialized design software.