Method for drawing rotating elliptical arc
Method for drawing rotating elliptical arc
 CN 101,625,765 B
 Filed: 08/18/2009
 Issued: 07/15/2015
 Est. Priority Date: 08/18/2009
 Status: Active Grant
First Claim
1. a method for drafting for rotating elliptical arc, is characterized in that, comprises following steps:
 Ellipse of revolution corresponding for rotating elliptical arc is decomposed into standard ellipse and this standard ellipse is transformed into the transformation matrix needed for this ellipse of revolution, the major axis of described standard ellipse or minor axis parallel are in transverse axis;
Determine to combine each point coordinate that described rotating elliptical arc is corresponding in described standard ellipse each point coordinate corresponding in described standard ellipse with described transformation matrix, obtain each point coordinate on rotating elliptical arc;
According to point coordinate each on described rotating elliptical arc, draw described rotating elliptical arc on a display screen.
Chinese PRB Reexamination
Abstract
The invention discloses a method for drawing rotating elliptical arc, including that a rotating ellipse corresponding to the rotating elliptical arc is divided into a standard ellipse (namely an ellipse major axis or minor axis of which is parallel to the horizontal axis) and the standard ellipse is transformed into a transformation matrix required to rotate the ellipse; a corresponding standard ellipse can be obtained according to the major axis or minor axis described by the rotating elliptical arc, coordinates of each point corresponding to the rotating elliptical arc on the standard ellipse are determined by the rotating elliptical arc, and the coordinates of each corresponding point on the standard ellipse are combined with the transformation matrix to obtain the coordinates of each point on the rotating elliptical arc; and the rotating elliptical arc is drawn on a display screen according to the coordinates of each point on the rotating elliptical arc. The rotating elliptical arc is fast drawn without establishing a mathematical model of the rotating ellipse.
7 Claims

1. a method for drafting for rotating elliptical arc, is characterized in that, comprises following steps:

Ellipse of revolution corresponding for rotating elliptical arc is decomposed into standard ellipse and this standard ellipse is transformed into the transformation matrix needed for this ellipse of revolution, the major axis of described standard ellipse or minor axis parallel are in transverse axis; Determine to combine each point coordinate that described rotating elliptical arc is corresponding in described standard ellipse each point coordinate corresponding in described standard ellipse with described transformation matrix, obtain each point coordinate on rotating elliptical arc; According to point coordinate each on described rotating elliptical arc, draw described rotating elliptical arc on a display screen.


2. the method for drafting of rotating elliptical arc according to claim 1, is characterized in that, is describedly decomposed into by ellipse of revolution corresponding for rotating elliptical arc in the step of standard ellipse and transformation matrix, comprises following substep:

A obtains the parameter of rotating elliptical arc to be drawn, and comprises the anglec of rotation of starting point coordinate, terminal point coordinate, the semimajor axis length of ellipse of revolution that this rotating elliptical arc is corresponding, semiminor axis length, this rotating elliptical arc; B, according to described starting point coordinate, terminal point coordinate and semimajor axis length, semiminor axis length, determines the standard ellipse that described rotating elliptical arc is corresponding; C, according to the anglec of rotation of described rotating elliptical arc, the starting point coordinate of described rotating elliptical arc and terminal point coordinate, determines the conversion starting point that described rotating elliptical arc is corresponding in described standard ellipse and conversion terminal; D, according to the origination data of the described anglec of rotation, described rotating elliptical arc and/or original equipment manufacturer coordinate, corresponding conversion starting point in described standard ellipse and/or conversion terminal point coordinate, determines that described standard ellipse is transformed to the transformation matrix needed for described ellipse of revolution;
Wherein, the transformation matrix between described standard ellipse and described ellipse of revolution is$\left\begin{array}{ccc}\mathrm{cos}\left(a\right)& \mathrm{sin}\left(a\right)& \mathrm{tx}\\ \mathrm{sin}\left(a\right)& \mathrm{cos}\left(a\right)& \mathrm{ty}\\ 0& 0& 1\end{array}\right;$ Tx is the coordinate figure moved horizontally, and ty is the coordinate figure of vertical movement, and a is the anglec of rotation of described rotating elliptical arc;
Described conversion starting point or conversion terminal are rotated a angle along initial point, obtain postrotational conversion starting point coordinate or postrotational conversion terminal point coordinate, the origination data coordinate of described rotating elliptical arc or original equipment manufacturer coordinate are deducted this postrotational conversion starting point coordinate or postrotational conversion terminal point coordinate, obtain the coordinate figure ty of coordinate figure tx and the vertical movement moved horizontally between described standard ellipse and ellipse of revolution.


3. the method for drafting of rotating elliptical arc according to claim 2, is characterized in that, in described step B, comprises following substep:
Described origination data coordinate, original equipment manufacturer coordinate and semimajor axis length, semiminor axis length are substituted into elliptic equation try to achieve the central coordinate of circle of described standard ellipse, determine the elliptic equation of described standard ellipse, wherein, described elliptic equation in, (x _{0}, y _{0}) representing the central coordinate of circle of described standard ellipse, a and b represents semimajor axis length and semiminor axis length respectively.

4. the method for drafting of rotating elliptical arc according to claim 3, is characterized in that, the central coordinate of circle of described standard ellipse is:

y _{0}=A+Bx _{0};
Or, y _{0}=A+Bx _{0};
Wherein, $A=\frac{{b}^{2}({{x}_{2}}^{2}{{x}_{1}}^{2})+{a}^{2}({{y}_{2}}^{2}{{y}_{1}}^{2})}{2{a}^{2}({y}_{1}{y}_{1})};$ $B=\frac{{b}^{2}({x}_{1}{x}_{2})}{{a}^{2}({y}_{2}{y}_{1})};$ C=b ^{2}+ a ^{2}b ^{2};
D=2a ^{2}(y _{1}A) B2b ^{2}x _{1};
E=a ^{2}(y _{1}A) ^{2}+ b ^{2}x _{1}^{2}a ^{2}b ^{2};
A and b represents semimajor axis length and semiminor axis length respectively, (x _{1}, y _{1}), (x _{2}, y _{2}) represent starting point coordinate and the terminal point coordinate of described rotating elliptical arc respectively;
The parameter of described rotating elliptical arc also comprises;
camber line size indicates, and is wideangle camber line or lowangle camber line for indicating described rotating elliptical arc;
Drawing hand designations, is clockwise direction or counter clockwise direction for indicating the origintodestination of described rotating elliptical arc;Indicate and described drafting hand designations according to described camber line size in described step B, uniquely determine the central coordinate of circle of described standard ellipse.

y _{0}=A+Bx _{0};

5. the method for drafting of rotating elliptical arc according to claim 2, is characterized in that, in described step C, comprises following substep:

According to origination data coordinate and the original equipment manufacturer coordinate determination straight line of described rotating elliptical arc, be rotated counterclockwise by this straight line, the angle of rotation is the anglec of rotation of this rotating elliptical arc; By postrotational straight line when slope is constant, crossing with standard ellipse, intersect 2 profound length formed and equal the profound length that described rotating elliptical arc origination data coordinate and original equipment manufacturer coordinate form, described crossing 2 be conversion starting point that described rotating elliptical arc is corresponding in described standard ellipse and convert terminal.


6. the method for drafting of rotating elliptical arc according to claim 5, it is characterized in that, equal the condition of the profound length of described rotating elliptical arc origination data coordinate and original equipment manufacturer coordinate formation in the profound length of described intersection point under, if the straight line crossing with described standard ellipse is more than one, then according to the anglec of rotation of described rotating elliptical arc, select a wherein described crossing straight line, uniquely determine the conversion starting point that described rotating elliptical arc is corresponding in described standard ellipse and conversion terminal.

7. the method for drafting of rotating elliptical arc according to claim 2, is characterized in that, the parameter of described rotating elliptical arc also comprises:
 camber line size indicates, and is wideangle camber line or lowangle camber line for indicating described rotating elliptical arc;
Drawing hand designations, is clockwise direction or counter clockwise direction for indicating the origintodestination of described rotating elliptical arc;Describedly determine in the step of each point coordinate that rotating elliptical arc is corresponding in described standard ellipse, indicate and described drafting hand designations according to the conversion starting point determined in the standard ellipse determined in described step B, described step C and conversion terminal, described camber line size, obtain each point coordinate that described rotating elliptical arc is corresponding in described standard ellipse.
 camber line size indicates, and is wideangle camber line or lowangle camber line for indicating described rotating elliptical arc;
Specification(s)