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Translated from: http://www.metro-hs.ac.jp/rs/sinohara/zahyou_rot/zahyou_rotate.htmTranslation: Tang YongkangSource: Http://blog.csdn.net/tangyongkangPlease specify the source1 rotation around the origin pointFor example, in 2-D coordinates, there is a point P (x, y), a linear opの length of R, and a straight angle between the linear op and the x-axis. The line op rotates in a counterclockwise direction around the origin, reaching P ' (s,t)s = R cos (A

1. Fill in the blanks(1) $\frac12 F ' (X_0) $To make $x =x_0+ \delta x$, the\[\mbox{native}=\lim_{\delta x\to 0}\frac{F (x_0 +\frac{\delta x}{2})-F (x_0)} {\delta X}=\frac12\lim_{\delta x\to 0}\frac{F (x_0 +\frac{\delta x}{2})-F (x_0)} {\frac{\delta x}{2}}=\frac12 F ' (X_0).\]If not strictly utilized on $x $ Rockwell can be seen more intuitively\[\mbox{Native}=\lim_{x\to X_0}\frac{\frac12 F ' (\frac{x+x_0}{2})} {1}=\frac12 F ' (X_0).\](2)-4Because\[\frac{2}{x^3} f ' (\frac{1}{x^2}) =\frac1x,\]So

1. Fill in the blanks(1) $\frac12 F ' (X_0) $To make $x =x_0+ \delta x$, the\[\mbox{native}=\lim_{\delta x\to 0}\frac{F (x_0 +\frac{\delta x}{2})-F (x_0)} {\delta X}=\frac12\lim_{\delta x\to 0}\frac{F (x_0 +\frac{\delta x}{2})-F (x_0)} {\frac{\delta x}{2}}=\frac12 F ' (X_0).\]If not strictly utilized on $x $ Rockwell can be seen more intuitively\[\mbox{Native}=\lim_{x\to X_0}\frac{\frac12 F ' (\frac{x+x_0}{2})} {1}=\frac12 F ' (X_0).\](2)-4Because\[\frac{2}{x^3} f ' (\frac{1}{x^2}) =\frac1x,\]So

the angle is 90 degree, which means a right angle is formed and the direction is completely different. If the angle is 180 degree, meaning the opposite direction. Therefore, we can determine the similarity of vectors by the angle. The smaller the angle, the more similar . Another junior high school knowledge: cosine theorem(It should be junior high school) Assume thatAVector is[X1, Y1].BVector is[X2, y2] Then we can change the cosine theorem to the following form.

Direct and indirect illumination Our current task is to add indirect light on the basis of direct light and shadow, that is to say, we need to add other surface reflection light to our current vertex/pixel illumination. We can use the same method as path raytrace. First, our rendering formula is divided into two parts: Direct Illumination and indirect illumination. L = l1 + L2= L1 + hybrid BRDF * l (X1) * cos θ * V * D ω L1 indicates Direct Il

ABS () Seek absolute value ACOs () Seeking the inverse cosine ASIN () Ask for the inverse of the string Atan () Ask for anyway cut ATAN2 () To find the tangent, to determine the quadrant by symbol Ceil () Minimum integer (for upper bound) not less than a value cos () Find cosine Cosh () Find hyperbolic cosine

) To change the color, add the relevant string to the following tag pairs:X=0:0.01:10;Plot (X,sin (x), ' R ')4) To change both the color and the Linetype state (line style), you can also add the relevant strings to the coordinate pairs:Plot (X,sin (x), ' r* ')5) Use Axis ([Xmin,xmax,ymin,ymax]) function to adjust the range of the axisAxis ([0,6,-1.5,1])6) Matlab can also add various annotations and processing of graphics: (see table above)Xlabel (' x-axis '); % x Axis annotationsYlabel (' Y axis

be represented by a single matrix. The three axes of the coordinate system, X, Y, z, x and y, respectively, are rotation axes, and the points are actually only two-dimensional rotations on the vertical axis. The three-dimensional rotation transformation matrix can be directly introduced with the two-dimension rotation formula. In the right-hand coordinate system, the positive direction of the object rotation is the right-hand helix direction, that is, from the positive half-axis of the axis to

SQL statements: Select Location.* from (select *,round (6378.138*2*asin (sqrt () (Pow () (Sin (36.668530*pi ()/180-px_lat*pi ()/180)/2), 2) +cos (36.668530*pi ()/180) *cos (Px_lat*pi ()/180) * POW (Sin ((117.020359*pi ()/180-px_lon*pi ()/180)/2), 2)) (*1000)) As distance from bsx_training where (px_state = 1) and (type_id! = ") and (((Px_lat >= 27.683290277922) and (px_l At Ignore the above SQL statement f

transformations, it is necessary to use transform: matrix(a,b,c,d,e,f) this transformation matrix. The 6 variables here make up a 3-medium transformation matrix. The translation, rotation, and scaling transformations of any point P (x, y) and their various combinations can be achieved through this transformation matrix: Note: Here we use homogeneous coordinates to express a point. Simply put, p (x, y) is expressed as P ' (x ', y ', 1) Translation matrix V (x, y) pans the TX along the x-axis, tr

Public Sub dorotate (Optional ByVal rotaryangle as Long = 0) ' Rotation at any angleDim Sdib as New CdibDim sbits () as RgbquadDim dbits () as RgbquadDim Stsa as Safearray2dDim DtSA as Safearray2dDim Lev as LongDim Wgt as LongDim x as LongDim y as LongDim Neww as Long, W as LongDim Newh as Long, H as LongDim F1 as double, f2 as doubleIf (m_hdib ' +++++++++++++++Dim OldWidth, oldheight as IntegerDim Newwidth, newheight as IntegerDim Theta as DoubleDim dx, dy as singleDim dxx, dyy as IntegerDim rx

[0, 2 * Pi] (2) Move the vertex along any orientation and a cylindrical surface can be generated.Translate = dir [0, 1, 0], DIS [0, 5] (3) scale the vertices on the curve based on any point in the spaceScale = anchor [0, 0, 0], X [1, 0], Z [1, 0] Finally, a dimension data is added from the curve to the surface, and the data size needs to be set: surface_slices = 72 The following shows the graphics and script code generated using these new statements: Circular Surface vertices = 360u = from 0 t

The three-leaf knot mentioned in the previous section is completely different from three to infinite. This section describes the n-leaf knot. Let's look at the formula for the three-leaf knot again: X = sin (t) + 2 * sin (2 * t)Y = cos (t)-2 * Cos (2 * t) Change it: X = sin (t) + 2 * sin (n-1) * t)Y = cos (t)-2 * Cos