Zhikai Wang Homepage

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	The Lorenz System This problem is studied as part of Zhikai Wang's master research. The computation tool is AUTO. Under the direction of the supervisor and by extending AUTO demos, some results are obtained. For example the 1,024 heteroclinic connections for some specific parameter settings. 1. Formalization of the system 2. Compute the stable manifold of the origin by AUTO It gives a better sense of how a planar disc 'rolls' under the evolution laws. At the same time, we also see clearer the role that 'rho' plays. Put two manifolds, rho=15 and rho=60, in the same scene. The symbols sequence of heteroclinic connections, rho=28. Does it show the Poincare sections of the unstable manifolds of the secondary equilibria? That reminds me `Zhou Yi', ``Taichi sheng liang yi...''. 3. There are more discussions in my master thesis Of course, there are numerous literatures for this problem.
	The CR3BP (The Circular Restricted Three-Body Problem) 1.Formalization of the system 2.Some computational results by AUTO An unstable manifold of family H1 and an invariant torus. A heteroclinic connection between familty L1 and L3. A homoclinic connections of family L3. 3. There are more discussions in my master thesis
	Depth peeling transparency GPU,GLSL,OPENGL,GTS,MULTI-PASS-Rendering, Depth peeling transparency 1. A simple glsl Phong shadin 2. The first niave attempt of peeling and blending 3. With bugs fixed, we try to blend 3 layers. 4. At this step we can render n layers. But for more than five layers, the effect won't be obvious.
	Real-time caustics GLSL, ray tracing, model view/world view, transformation, GTS model 1. Course project of Concordia graduate course COMP 7661 2. Many bugs are fixed after the course. But there are still issues to be sovled. 3. We may say the results are something resembling the caustics.