sin(​sqrt(​x^​2+​y^​2))/​sqrt(​x^​2+​y^​2) Castle Topper

thingiverse

A showstopper for showcasing your mathematical expertise while crafting an impressive castle! Based on a 3D projection of the equation Z = sin(​sqrt(​x^​2+​y^​2))/​sqrt(​x^​2+​y^​2), simply fill the mold with moist sand and attach it to your castle for a fantastic focal point! When I came across this challenge, I knew I wanted to develop an engaging and interactive way to visualize mathematics in three dimensions, making it look truly amazing was just a bonus! To create this model, I utilized Blender 3D modeling software, subdivided a plane into approximately 65k vertices, and set each vertex to its corresponding position when inputted into the formula. From there, all I did was design the mold around the function. Unfortunately, where I reside, I didn't have access to any sand for molding, so I used brown sugar instead. Edit: Added a solid version for those who prefer a neat model of the function. Edit (7/31/15): Created and uploaded a much cleaner and more useful version, it prints without support and allows a cleaner sand mold, plus this one actually works in slic3r. Edit(7/14/15): Developed a version with the function on the side.