A second order geometric method for ray/parametric surface intersection

TL;DR: The method is simpler than existing methods for it merely concerns first-order information of the surface, if it only asks for linear convergence, and has better error control mechanism, if the authors seek for second-order convergence.

TL;DR: The main ideas are adopting a scheme tracing along the surface to obtain a good initial point, which is close to the desired point with any prescribed precision, and conducting Newton iteration process with the point as a start point to compute desired parameters.

TL;DR: Free-form surfaces and implicit surfaces must be tessellated before being rendered with rasterization techniques, but ray tracing provides the means to directly render such objects without the need for translation.

TL;DR: A new method for inverse geometric reconstruction of conics in 3D space using a ray–surface intersection that requires only three intersection points and does not require to establish correspondence between the two perspective views.

TL;DR: Consideration of all of these factors allows the shader to accurately simulate true reflection, shadows, and refraction, as well as the effects simulated by conventional shaders.

TL;DR: This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces.

TL;DR: A Algorithmic Aspects of Geometric Modelling and Representation of Multiply Continuous Functions in the Unit Domain and some Remarks on Cyclides in Solid Modeling.

TL;DR: A method for using ray tracing to render spline surfaces that is suitable for any object generated from control vertices via tensor-product B-splines, and makes use of kajiya's work on ray tracing procedurally defined surfaces.