已知椭圆中心和椭圆上四点求绘制椭圆。

cable2004

已知椭圆中心和椭圆上四点求绘制椭圆。

highflybir

恐怕此题有些问题，如果已知椭圆的中心，只是再需要椭圆上三点，就可以确定一个椭圆了。你给的条件冗余了。
也许是我想错了。

cable2004

任意4点，好像需要4个吧！3个当然更好！

qjchen

http://bbs.mjtd.com/forum.php?mo ... 8069&fromuid=250774

http://bbs.mjtd.com/forum.php?mod=viewthread&tid=62903&page=1#pid335227

是这个解答么

highflybird

cable2004 发表于 2012-2-2 17:56
任意4点，好像需要4个吧！3个当然更好！

如果已知了椭圆中心，应该只是需要三点就可以了，而且这三点还要满足一个条件。即这三点的任意一点 不能落在其他两点和椭圆中心组成的三角形内（构成凹四边形）.
方程解法已经有了，至于其几何画法暂时未想出。

cable2004

那可以求出长轴 ，短轴吗？

qjchen

http://bbs.mjtd.com/forum.php?mo ... mp;page=1#pid408069

http://bbs.mjtd.com/thread-77145-2-1.html

假如你只是需要用计算公式或者Lisp编程写出这个代码的话，应该第一个帖子就可以了

假如你需要用尺规作图的方法来求出这个问题的话，19世纪有位Thomas Henry Eagles大师

写的  Constructive geometry of plane curves. With numerous examples 书中给出了方法，你若需要的话，我可以用cad绘制并解释一下
这本书可是绝好的书啊，国内其实应该组织翻译一下的

书中给出了下列各种情况的几何作图方法，其中的一些情况论坛讨论过，如
http://bbs.mjtd.com/thread-76826-1-1.html

其他的一些内容，可以参考Geometry Express （国内翻 几何表达式）网站上的这个地方
http://sylvester.math.nthu.edu.t ... /Ellipse1/part2.htm

应该基本涵括了绘制椭圆的大部分情况了吧
Construction 1
Given axes, construct an ellipse         
Construction 2
Given a pair of conjugate diameters, construct the axes of an ellipse
Construction 3
Given a pair of conjugate diameters, construct an ellipse
Construction 4
Construct an ellipse with a given axis to pass through a given point
Construction 5
Construct an ellipse with a given axis to touch a given line
Construction 6
Construct an ellipse, the directions of a pair of conjugate diameters, a tangent and its point of contact being given
Construction 7
Construct an ellipse, the center, two points on the curve and directions of a pair of conjugate diameters being given
Construction 8
Construct an ellipse, the center, the directions of the major axis and two tangents being given
Construction 9
Construct an ellipse, the center, the directions of a pair of conjugate diameters, a tangent and a point on the curve being given
Construction 10
Construct an ellipse, the center, two tangents and a point on the curve being given
Construction 11
Construct an ellipse, the center, three tangents being given
Construction 12
Construct an ellipse, the center, two points on curve and a tangent being given
Construction 13
Construct an ellipse, the center, three points on the curve being given
Construction 14
Construct an ellipse, the foci and a point on the curve being given
Construction 15
Construct an ellipse, the foci and a tangent to the curve being given
Construction 16
Construct an ellipse, a focus, a tangent with its point of contact and second point on the curve being given
Construction 17
Construct an ellipse, a focus, a tangent and two points on the curve being given
Construction 18
Construct an ellipse, a focus, a point on the curve and two tangents being given
Construction 19
Construct an ellipse, a focus and three tangents being given
Construction 20
Construct an ellipse, a focus and three points being given
Construction 21
Construct an ellipse, two tangents with their points of contact and a third point being given
Construction 22
Construct an ellipse, two tangents and three points being given
Construction 23
Construct an ellipse, three tangents and two points being given
Construction 24
Construct an ellipse, five tangents being given
Construction 25
Construct an ellipse, four tangents and a points being given
Construction 26
Construct an ellipse, five points being given
Construction 27
Construct an ellipse, four points and a tangent being given
Construction 28
Construct the center of curvature at any point of a given ellipse

highflybird

用lisp程序解决的：
加载程序或者把文件拖入CAD绘图区，运行命令：test

highflybird

由程序看来，如果已知中心，需要其他三点才能确定椭圆。多了点就冗余了。
有些情况下，无法生成椭圆。

cable2004

谢谢highflybird ，向你学习！