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, V = (V1, V2), W = (W1, W2 ); This definition can be applied from two-dimensional space to three-dimensional and other high-order spaces. We know that p (x, y) on a two-dimensional plane rotates an angle α on the coordinate axis, and the new coordinate is P (xnew, ynew) If the distance from point P is R, and the angle between the point and the original X axis is delta X = rcos delta, y = rsin delta; The new coordinates can be obtained: xnew = rcos (delta-α) = rcos Delta

that I can use the sine wave mentioned above to create a rectangular wave with a 90 degree angle, will you believe it? You won't, just like me. But let's see: The first figure is a depressing sine wave cos (X) The second figure is the superposition of two cute sine waves cos (x) + A. Cos (3x) The third figure is the superposition of four spring sine waves. The

\[v=\int_0^{4} \pi (4-y) dy =8 \pi.\]4. According to the question set, to $x $ for the integral variable, the observation image we just need to calculate $x $ from $0$ to $\pi a$, and then multiplied by two\[dv= [\PI (2a) ^2-\pi y^2 (x)] dx\]The\[v= 2\int_0^{\pi A} [\pi (2a) ^2-\pi y^2 (x)] DX.\]Using parametric equations to\[v= 2\int_0^{\pi} [\PI (2a) ^2-a^2 (1-\cos t) ^2]d (A (T-\sin t))= 2\pi a^3 \int_0^{\pi} [(1-\

domain is Fourier analysis of crossing. Fourier analysis can be divided into Fourier series (Fourier Serie) and Fourier transform (Fourier transformation), we start from a simple beginning.Spectrum of the second, Fourier series (Fourier series)Or a chestnut and a picture of the truth to understand.Would you believe me if I said I could stack a rectangular wave with a 90-degree angle with the sinusoidal wave I said earlier? You won't, just like I was when I was. But look at:The first picture is

rotation angle θ to obtain the coordinate (x', y') of p ').As you can see from Figure 4.2, x' = OB, y' = BP '. Therefore, the problem is to find the length of OB and BP. Figure 4.2 Rotation Transformation First, the distance from the point to O remains unchanged during the rotation process, that is, OP = op '. We set op = op '. Then, we examine the triangle OBF and the triangle p'cf, the angular ofB = Angular p'fc, the angular FBO = Angular P' cf = 90 degrees, and the inner angle and theorem o

. The Deriv () function returns an expression type variable and then runs the expression with the Eval () function to get the result, as the above code does.If you want to call the calculation formula as a function, you also need to pass the third parameter Func and let the Func parameter be true, as the following code implements.Calculates the derivative of the sine function y=sin (x), which is calculated according to the derivative formula, for the manual calculation of the deformation result

frequency of: fn= (n-1) *fs/n.As can be seen from the above formula, FN can distinguish the frequency as fs/n, ifSampling frequency FS is 1024Hz, the sample number is 1024 points, you can distinguish to 1Hz.1024Hz sample rate of 1024 points, just 1 seconds, that is, the sample 1 secondsTime signal and do the FFT, the result can be analyzed to 1Hz, if the sample 2 secondsSignal and do the FFT, the result can be analyzed to 0.5Hz. If you want to increase the frequencyResolution, you must add a sa

spectrum is converted to a [-PI,PI] interval, which is the actual situation (the DTFT of discrete aperiodic signals is continuous cycle, With 2pi as the cycle) %%%%%% (2) discrete period%%%%%%%%%%%%% x =cos (PI/8*N+PI/3) +0.5cos (7*PI*N/8);(spectrum for discrete periods (periodic base wave period N)) %%%%%%%% determines that the fundamental period of the signal is 16. N = 16; n = 0:n-1; x = cos (PI/8*N+PI

Since the electronic equipment gradually entered our life began, as long as the "domestic" with the side of the matter has been very affecting the people's hearts. For example, a few days ago, the Chinese Academy of Sciences Software and Shanghai Lian Tong Company jointly released the so-called with independent intellectual property rights of the COS (China operating system) systems, it caused a exclaim. This is certainly a lot of exclamation is the

latitude and longitude coordinates In actual Web development, there are more and more professional algorithms in some specific fields. For example, the distance calculation method mentioned in this article is based on two dimensions. Two common computations: 1. The distance to be calculated is the elliptical distance. Set the longitude and latitude of the first Vertex A to (LonA, LatA), and the longitude and latitude of the second vertex B to (LonB, LatB) based on the zero-degree longitude line

After the image is stretched, we naturally want to rotate the image. We found the formula for image rotation: X' = x cos θ-y sin θ; Y' = x sin θ + y cos θ; This image formula can be used in high school mathematics. Then we need to expand because we do not rotate at the origin. We need to rotate around the original image center. Then we assume that the original image center is oldcenterx and oldcentery. af

In the past, I was naive to think that it was nothing more than calculating the distance one by one, and then comparing them out. When there were a lot of users accessing the database and there was a lot of latitude and longitude information in the database, the rapid increase in computing workload can make the server completely dumb, or the experience of the old generation is richer than ours, which gives me a lot of inspiration. SQL statement query latitude and longitude range specify a latit

Circle vertices = 360w = from 0 to (2*PI)r = 10.0x = r*sin(w)y = r*cos(w) Circular Surface with texture coordinates and vertices vertices = D1:360 D2:100u = from 0 to (2*PI) D1v = from 0 to 10 D2x = sin(u)y = cos(u)r = (x+1)/2g = (y+1)/2b = v/10x = v*xy = v*y Elliptic vertices = 1000r = 10.0e = 0.75t = from 0 to (2*PI)p = r/(1.0 - e*cos(t))x = p*sin(t)y = p*

/from quaternions1Quaternion from Axis-Angle // Convert from axis angleVoid quaternion: fromaxis (const vector3 V, float angle){Float sinangle;Angle * = 0.5f;Vector3 VN (v );Vn. normalise (); Sinangle = sin (angle ); X = (VN. x * sinangle );Y = (VN. y * sinangle );Z = (VN. z * sinangle );W = cos (angle );} Quaternion from Euler Angles // Convert from Euler AnglesVoid quaternion: fromeitch (float pitch, float yaw, float roll){// Basically we create 3