Chương 4. Các thuật toán Vertex và Pixel Shader
light vector. Vector hướng ánh sáng trong không gian tiếp tuyến (tangent space), vector này được tính trong Vertex Shader và được truyền vào Pixel Shader để sử dụng. view vector. Vector tính từ mắt đến điểm nhìn (tọa độ trong không gian tiếp tuyến), vector này được tính trong Vertex Shader và truyền vào Pixel Shader để sử dụng. specular constant. Hằng phản chiếu, giá trị càng lớn thì vùng phản chiếu càng nhỏ. specular lookup.
Institute for Theoretical Physics University of California Santa Barbara, CA 93106 email@example.com December 1997
Abstract These notes represent approximately one semester’s worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein’s equations, and three applications: gravitational radiation, black holes, and cosmology. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/notes/.
Table of Contents
Classical differential geometry is the approach to geometry that takes full
advantage of the introduction of numerical coordinates into a geometric
space. This use of coordinates in geometry was the essential insight of Rene
Descartes that allowed the invention of analytic geometry and paved the way
for modern differential geometry. The basic object in differential geometry
(and differential topology) is the smooth manifold. This is a topological
space on which a sufficiently nice family of coordinate systems or "charts"
This is a quick set of note on basic differential topogoly. It get sketchier as it goes on. The last few section are only introduce the terminology and the some of concepts. These note qre written faster than I can read and may make no sense in spots.
Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: An Introduction to Relativity 8.
simple closed c. ®−êng ®ãng ®¬n sine c. ®−êng sin sinistrorsal c. ®−êng xo¾n tr¸i skew c. hh. ®−êng lÖch space c. hh. ®−êng ghÒnh star-like c. ®−êng gièng h×nh sao stress-train c. ®−êng øng suÊt biÕn d¹ng syzygetic c. ®−êng héi xung, ®−êng xiziji tangent c. ®−êng tiÕp xóc three leaved rose c. ®−êng hoa hång ba c¸nh trannsendental c. ®−êng siªu viÖt transition c. ®−êng chuyÓn tiÕp triangular symmetric c. ®−êng ®èi xøng tam gi¸c trigonometric(al) c. ®−êng l−îng gi¸c twisted c.
Invariant measures for the geodesic ﬂow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this ﬂow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces.