Projection Mapping Second pass WIP

In recent years, the art of 3D projection mapping has been climbing in popularity. According to Wikipedia, 3D projection mapping is defined as “any method of mapping three-dimensional points to a two-dimensional plane.” The most common form of this technique is the mapping of geometrical shapes and architectural facades. These 3D projections give artists the power “change” the objects surface and create illusions of depth, forced perspective as well as more dramatic special effects such as objects crumbling, morphing and turning into cloth. However before these artistic visualizations can be realized, you must understand how the mapping process works and that is what I have been researching in recent weeks.
Initially my knowledge of the projection process was very limited. I was not aware of the intricacies of process that were necessary for accurate projections. I was under the impression that if and object was accurately replicated in 3D software it was merely the act of matching the digital camera position with the projectors position in real space that would allow effective mapping. I soon learned that these notions were incorrect. While struggling to align our 3D rendered models with real world objects, we bypassed the process by manipulating geometries to make up for our miscalculations. However, we soon realized that while this may work for static projections, animation would likely expose the flaws in our process.
Creating an accurate and intuitive method for mapping these projections became imperative and Matt, Ben and I began experimenting. We decided to start simple by projecting onto a single flat surface in the hopes that what we discovered could translate into more complicated perspective projections. The first step was accurately measuring our rectangular box: 77.75w x 30”h x 18”d. With these measurements we were able to create a replica within Maya. The next step was to translate the distance between real-world projector and object to our digital camera and 3D object. The projector was placed perpendicular to the box and at a distance of 144.5 inches measured from lens to the box’s projector facing side. The virtual box’s position in was coordinates (xyz) 0,15,0. Since the box is 30 inches high chose its Y position 15 inches above the ground plane which put the box’s bottom flush with the floor. The camera was created and placed 144.5 in. away from the virtual box facing side which would put it 154.5 in. away from the 0,0,0 origin. The physical projector lens was measured 3.25 inches off the ground so we also bumped the digital camera up 3.5 in. in the Y direction.
After figuring the spatial relationships in physical and digital space it was necessary to adjust the digital camera’s Focal Length, Angle of View, Aperture Settings etc. to match that of our projector. These settings are projector specific and in this case we were using a Canon ______. The angle of view was calculated by projecting onto a close, perpendicular service so that the projection was square. We measured first the distance from projector lens to the center of the projection to get the adjacent side (X). Then we measured the width of the projector and divided it by two to get our opposite side (Y). Using the Pythagorean theorem we found the Hypotenuse (H). The tan ø =y/x, or our FOV angle =2* arctan (y/x).

The focal length was actually found in the Canon Owners manual which was 34.5. I believe that only one of these numbers needs to be found because their values directly correlate to one another. We used the found focal length since it was the most accurate and plugged it into our digital camera’s focal length value. However, manuals usually give you a focal length range to account for the zoom settings of the projector. We assumed that since we were zoomed all the way in, we would use the larger focal length. We discovered later that it was the smaller of the two numbers we should have used.