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Determine Perspective Lines With Off-page Vanishing Point

In perspective drawing, a vanishing point represents a group of parallel lines, in other words, a direction. For any point on the paper, if we want a line towards the same direction (in the 3d space), we simply draw a line through it and the vanishing point. But sometimes the vanishing point is too far away, such that it is outside the paper/canvas. In this example, we have a point P and two perspective lines L1 and L2. The vanishing point VP is naturally the intersection of L1 and L2. The task is to draw a line through P and VP, without having VP on the paper. I am aware of a few traditional solutions: 1. Use extra pieces of paper such that we can extend L1 and L2 until we see VP. 2. Draw everything in a smaller scale, such that we can see both P and VP on the paper. Draw the line and scale everything back. 3. Draw a perspective grid using the Brewer Method. #1 and #2 might be quite practical. #3 may not guarantee a solution, unless we can measure distances/p...

[转] UTF-8 and Unicode FAQ for Unix/Linux

这几天,这个东西把我搞得很头疼而且这篇文章好像太大了,blogger自己的发布系统不能发只好用mail了 //原文 http://www.cl.cam.ac.uk/~mgk25/unicode.html UTF-8 and Unicode FAQ for Unix/Linux by Markus Kuhn This text is a very comprehensive one-stop information resource on how you can use Unicode/UTF-8 on POSIX systems (Linux, Unix). You will find here both introductory information for every user, as well as detailed references for the experienced developer. Unicode has started to replace ASCII, ISO 8859 and EUC at all levels. It enables users to handle not only practically any script and language used on this planet, it also supports a comprehensive set of mathematical and technical symbols to simplify scientific information exchange. With the UTF-8 encoding, Unicode can be used in a convenient and backwards compatible way in environments that were designed entirely around ASCII, like Unix. UTF-8 is the way in which Unicode is used under Unix, Linux, and similar systems. It is now time to make sure that you are well familiar ...

Moving Items Along Bezier Curves with CSS Animation (Part 2: Time Warp)

This is a follow-up of my earlier article. I realized that there is another way of achieving the same effect. This article has lots of nice examples and explanations, the basic idea is to make very simple @keyframe rules, usually just a linear movement, then use timing function to distort the time, such that the motion path becomes the desired curve. I'd like to call it the "time warp" hack. Demo See the Pen Interactive cubic Bezier curve + CSS animation by Lu Wang ( @coolwanglu ) on CodePen . How does it work? Recall that a cubic Bezier curve is defined by this formula : \[B(t) = (1-t)^3P_0+3(1-t)^2tP_1+3(1-t)t^2P_2+t^3P_3,\ 0 \le t \le 1.\] In the 2D case, \(B(t)\) has two coordinates, \(x(t)\) and \(y(t)\). Define \(x_i\) to the be x coordinate of \(P_i\), then we have: \[x(t) = (1-t)^3x_0+3(1-t)^2tx_1+3(1-t)t^2x_2+t^3x_3,\ 0 \le t \le 1.\] So, for our animated element, we want to make sure that the x coordiante (i.e. the "left" CSS property) is \(...

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