# patches

1. ### A cloak covered with patches

Hi. Could you help me solve this problem. I've tried using inclusionâ€“exclusion principle but it didn't work. There is a cloak which area equals 1. It is completely covered with 5 patches, whose area is at least 0,5. Show that the area of the intersection of certain two patces is at least 0,2...
2. ### How to connect cubic bezier surface patches continuous upto the 2nd derivative

Hi, Imagine that I have got 16 nodes in a 3D space, each node with its (x,y,z) coordinates. The nodes are ordered in a grid and numbered (i,j) in accordance with their position, so i\in[1,4] and j\in[1,4]. I also know that the nodes are part of a curved surface (a topological square) and that...
3. ### coordinate patches?

The hyperboloid is given by H=\{(x,y,z) \vert x^2 + y^2 - z^2 =1\}. Find coordinate patches that cover all of H, using the parametrization \textbf{H}(s,t)=(\cos s \, \sec t ,\, \sin s \, \sec t ,\, \tan t). First thing--we haven't covered "coordinate patch" in lecture, and the phrase does not...