详解椭圆弧组码41的含义

newer · 发表于 2014-12-20 13:00:49

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Explanation of elliptical arcs group code 41

Question
In elliptical arcs, group code 41 is described as the start parameter. However,
it doesn't seem to be associated with any of the known values for the arc. How
is this value derived?
Answer
An elliptical arc is a special version of an arc that follows the eccentricity
of the ellipse. One way to generate this type of arc is to find the parametric
normal of the starting point. To do so, you must specify a start angle that is
different from the actual start angle of the drawn arc. Group code 41 contains
this parametric angle expressed in radians.

WHAT IS THE PARAMETRIC ANGLE?

The parametric angle is generated from two concentric circles whose center is
the center of the ellipse and whose radii are the major and minor axes,
respectively. Every point of the ellipse lies either between or on these two
circles, and each elliptical point can be defined by a unique relation to them.
To discover this relationship, draw a line perpendicular to the major axis from
a point on the ellipse to the closest intersection with the circle described by
the major axis. Then do the same with the minor axis, starting from the
elliptical point and drawing perpendicular to the minor axis until the line
intersects the circle described by the minor axis. The two points of
intersection with the circles are colinear with the center of the ellipse. The
angle between the line containing these three points and the major axis is the
parametric angle specified by group code 41.

HOW DO I CALCULATE IT FROM THE TRUE START ANGLE?

To calculate the parametric angle from the true start angle, you must first find
the start point on the ellipse. This requires a simultaneous solution to the
equations for the line and the ellipse. In this example we assume that the major
axis of the ellipse lies on the x-axis with the origin at the center of the
ellipse. When this point is found, you can use its y-value and the minor axis to
solve the equation for the circle whose radius is the minor axis value and whose
center is the center of the ellipse. This will provide the x,y point on the
circle that dictates the parametric angle from the center of the ellipse.

The following is an AutoLisp example that demonstrates how to use trigonometric
functions to determine the parametric angle:

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lucas3 · 发表于 2014-12-20 13:42:58

谢谢分享！

819534890 · 发表于 2014-12-20 14:04:33

谢谢分享。

HLCAD · 发表于 2014-12-20 14:38:45

向N版学习ing...

wzg356 · 发表于 2014-12-20 15:28:09

太深，不懂
纯顶

/db_自贡黄明儒_ · 发表于 2014-12-20 19:39:23

E文叙述一大篇，结论复杂不？

sicky111 · 发表于 2014-12-25 18:01:05

就算看不懂也要支持。

e2002 · 发表于 2014-12-31 21:47:26

感谢分享，学习中。

yularna · 发表于 2015-1-1 13:17:38

好好学习，天天向上！

qyming1996 · 发表于 2015-1-2 10:15:58

学习。。。。。。。。。。。。。。

adslwang · 发表于 2015-1-6 07:30:26

向N版学习好好学习，天天向上！

ynhh · 发表于 2017-3-10 10:08:04

感谢N版的分享

434939575 · 发表于 2018-4-1 21:24:25

进来看看，今天想椭圆弧转圆弧..

7325pink · 发表于 2018-4-2 07:19:15

谢谢分享！支持！

beiy012 · 发表于 2018-4-3 12:25:23

谢谢分享！！！

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