geometry for idiots

' =rcos (\theta+\alpha) $$$ $y ' =rsin (\theta+\alpha) $$Open to get:$ $x ' =r (Cos{\theta}cos{\alpha}-sin{\theta}sin{\alpha}) =xcos{\alpha}-ysin{\alpha}$$$ $y ' =r (Sin{\theta}cos{\alpha}+cos{\theta}sin{\alpha}) =xsin{\alpha}+ycos{\alpha}$$That$ $x ' =xcos{\alpha}-ysin{\alpha}$$$ $y ' =xsin{\alpha}+ycos{\alpha}$$1 vt rotate (vt A,doublereturn VT (A.x*cos (RAD)-a.y*sin (RAD), A.x*sin (RAD) +a.y*cos (RAD))}View Code5. pluralPetition mentioned, but I don't know what to do ... Seemingly also relat

Introduction of the concept of cross-product:In order to measure the tilt state of a straight line in the plane, we introduce the concept of inclined angle. By establishing tanα= K in a Cartesian coordinate system, we realize the connection between geometric relations and algebraic relationships, which in fact is a core of solving geometrical problems with computers, and the computer is doing numerical operations, so what you need to do is to express the relations in algebraic relation. In space

ACM Computational Geometry topic RecommendationI. Point, line, face, Shape basic relation, point product understanding of the cross product POJ 2318 TOYS POJ 2398 Toy Storage Position of Point and segment POJ 3304 Segments Position of line and line POJ 1269 Intersecting Lines Straight position POJ 1556 The Doors Segment intersection + short

Before the computer room did not network to do this problem, with the analytic geometry to determine the intersection axis#include Hhh"Bzoj 1007" "Hnoi 2008" Horizontal linear analytic geometry

2 . Polygon(Polygon.pas/c/cpp)"Problem description"In a planar Cartesian coordinate system, a simple polygon [1] with a vertex transverse ordinate is given as an integer, and the number of points in the polygon where the horizontal ordinate is an integer is obtained.InputThe input file name is polygon.in, a total line, and the first line contains a positive integer.The following lines, each containing two integers, represent the coordinates of the polygon vertices in turn, and the vertices are g

Since I'm in charge of calculating geometry, I'll brush some more questions. WWTemplate adapted from RujiaPoint, line Base section:structpoint{Doublex, y; Point (Doublex=0,Doubley=0): X (x), Y (y) {}};typedef point Vector; Point Read () {DoubleX, Y;SCANF ("%LF%LF", x, y);returnPoint (x, y);} Vectoroperator+ (vector A, vector B) {returnVector (a.x + b.x, A.Y +b.y); }vectoroperator-(vector A, vector B) {returnVector (a.x-b.x, A.Y-b.y); }vectoroperator*

This article mainly introduces PHP using GD2 to draw the geometry, combined with the example form analysis of the common functions involved in GD2 drawing and specific use of skills, the need for friends can refer to the following This example describes how PHP uses GD2 to draw geometry. Share to everyone for your reference, as follows: You can use the GD2 function not only to draw line shapes, but also to

Geometric artboards can make a point move along a track, make static dynamic, draw beautiful, vivid dynamic graphics, and realize the animation effect. In the following, we will learn how to make the geometric artboard point animation by illustrating the animation on the line segment .　　The following steps are described:Open the geometry artboard, draw line AB in the work area, and draw a little C on line AB.　　Select Point C, click Edit--Action class

The idea of the problem is very good to think, divided into the following 4 steps:1: Seek the radius of the circumscribed garden2: Ask for three central angle3: Find the greatest common divisor of three center angle4: Greatest Common divisor is the largest regular polygon internal angle, to find the area can be.But every step does not beg ah .... Sad ... When I think of the 3rd step, I even feel that I should ask for it in another way. To change the method. The

Geometry Made Simple Geometry Made Simple Description Mathematics can be so easy when you have a computer. consider the following example. you probably know that in a right-angled triangle, the length of the three sides a, B, c (where c is the longest side, called the hypotenuse) satisfy the relation a * a + B * B = c * c. this is called Pythagora's Law. Here we consider the problem of computing the length

Test instructions: give four points, ask you whether the fourth point in the first three points constitute the circle, if the output of "Accepted" outside the circle, otherwise output "rejected", the title guarantee the first three points are not in a straight line. Analysis: A simple computational geometry problem, if you can know the center and radius (radius) and the distance between the fourth and center points (Distance), we can determine wheth

Abstract: Cgal is an open-source computational geometry library that logs its compilation, installation, and usage methods.1 Library DownloadSite: http://www.cgal.org/Download: Https://gforge.inria.fr/frs/download.php/file/34514/CGAL-4.5.2.zip2 extracting, compiling and installingShell into the Unzip folder1) Library configuration file Generation command:CMake.Tips for missing GMP and MPFR librariesInstall the Missing libraries:sudo apt-get install Li

are perpendicular and only when xaxb+yayb=0.Vector Length: Len (A) =sqrt (Dot (a,a)).Vector angle: Angle (A, b) =cos (Dot (b)/len (A)/len (A)).Cross product: Two vectors consisting of a triangular twice times the direction of the area, or called parallelogram. (The result is a vector, temporarily not to understand the direction of the problem)Cross (A, b) =xayb-xbya.Cross product is directed, the direction depends on sin (θ), along the first vector a See, B on the left side of the cross product

To give you illustrator software users to detailed analysis to share the creation of a beautiful seamless geometry of the production tutorial. Tutorial Sharing: ① Use the Ellipse tool (mouse-click the Rectangle tool to press and hold) to create two circles of different sizes, requiring the two centers to be located on the same vertical line. Select the two circles, then select Objects > Blends > Make or press CTRL +

To give you illustrator software users to the detailed analysis of the production of linear fringe geometric art patterns of the tutorial. Tutorial Sharing: First, create art brushes To make a stripe pattern, the first thing we need to think about is what tools are used to achieve it more quickly. Because such as stripes, dots, squares ... This kind of basic pattern has the common character that repeats a certain visual law, therefore, we can first establish this vis

Mike wants to prepare in IMO but he doesn ' t know geometry, so he teacher gave him an interesting geometry problem. Let's DEFINEF ([L, r]) = R-l + 1 To is the number of the integer points in the Segment[l, R] with L≤r (say that). You are given the INTEGERSN and K andn closed intervals [Li, RI] Onox axis and you had to find: In other words, you should find the sum of the number of the integer points in the

Air Hockey Time limit:1000ms Memory limit:262144kb 64-bit integer IO format:%lld Java class N ame: Main Special Judge prev submit status statistics discuss Next type: None N Onegraph theory 2-satarticulation/bridge/biconnected Component cycles/topological sorting/strongly Connected Component shortest Path bellman ford dijkstra/floyd Warshall euler trail/circuit heavy-light Decompositionminimum Spanning Tree stable marriage Problem treesdirected Minimum Spanning Tree flow/ Matching graph matc

This section is Rujia's "Algorithmic Competition Primer Classic" (first edition) Chapter III of Number theory and computational geometry, but do not need to use classical algorithms and templates to simulate the main Title Link: Http://acm.hust.edu.cn/vjudge/contest/view.action?cid=48182#overview Topic Analysis: a.uva575 Simple simulation gives you a number that allows you to find the answer to the conversion as required, except that the process of co

appears to be a superficial phenomenon, essentially a business model that Nokia has continued to monetize through its patented push-plate. In the author's view, this business model has certain feasibility, but there are certain risks, after all, only the licensing, Nokia how to monitor product quality is a big problem. Suppose the quality of the product is not well, unlucky or Nokia brand. Of course, Nokia can find a sustainable business model to solve the pressing problems, without compromisin

This article focuses on the intersection of line segments.Given two line segments, how can I tell if the two segments intersect?If the two segments intersect, how do you find the intersection?Line intersection problem is usually because of its complicated situation of the kind of people to avoid and far, here hope through the author's simplified discussion hope to help readers to comb the idea.First, we try to draw a few geometric images to find out the intersection of a number of different case