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2点間の距離、中点の座標を求める

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数学公式

平面上の2点 A(x1, y1), B(x2, y2) 間の距離は、
$$ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
中点の座標は、
$$ \left(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2} \right)$$


空間の2点 A(x1, y1, z1), B(x2, y2, z2) 間の距離は、
$$ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$$
中点の座標は、
$$ \left(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2},\frac{z_1 + z_2}{2} \right)$$


AutoLISPで求める

距離は distance 関数で求める。

;; 2点の中点を計算
(defun point:GetMidpoint (a b)
    (mapcar (function (lambda (a b) (/ (+ a b) 2.))) a b)
)
;; < Example >
;; 2D
(distance '(4 1) '(-1 4))
;; -> 5.83095
(point:GetMidpoint '(4 1) '(-1 4))
;; -> (1.5 2.5)

;; 3D
(distance '(-5 1 2) '(4 -1 -4))
;; -> 11
(point:GetMidpoint '(-5 1 2) '(4 -1 -4))
;; -> (-0.5 0.0 -1.0)

AutoCAD .NET(C#)で求める

2D点はPoint2d構造体、3D点はPoint3d構造体を使う。
距離は GetDistanceTo メソッドで求める。

// 2点の中点を計算(2D)
public static Point2d GetMidpoint2d(Point2d a, Point2d b) {
    return new Point2d((a.X + b.X) / 2, (a.Y + b.Y) / 2);
}

// 2点の中点を計算(3D)
public static Point3d GetMidpoint3d(Point3d a, Point3d b) {
     return new Point3d((a.X + b.X) / 2, (a.Y + b.Y) / 2, (a.Z + b.Z) / 2);
}

// < Example >
// 2D
var pt2d1 = new Point2d(4, 1);
var pt2d2 = new Point2d(-1, 4);
pt2d1.GetDistanceTo(pt2d2);
// -> 5.83095
GetMidpoint2d(pt2d1, pt2d2);
// -> (1.5, 2.5)

// 3D
var pt3d1 = new Point3d(-5, 1, 2);
var pt3d2 = new Point3d(4, -1, -4);
pt3d1.GetDistanceTo(pt3d2);
// -> 11
GetMidpoint3d(pt3d1, pt3d2);
// -> (-0.5, 0.0, -1.0)

ObjectARX(C++)で求める

2D点はAcGePoint2dクラス、3D点はAcGePoint3dクラスを使う。
距離は distanceTo メソッドで求める。

// 2点の中点を求める (2D)
satic AcGePoint2d getMidpoint2d(AcGePoint2d a, AcGePoint2d b) {
    return AcGePoint2d((a.x + b.x) / 2, (a.y + b.y) / 2);
}

// 2点の中点を求める (3D)
static AcGePoint3d getMidpoint3d(AcGePoint3d a, AcGePoint3d b) {
    return AcGePoint3d((a.x + b.x) / 2, (a.y + b.y) / 2, (a.z + b.z) / 2);
}

// < Example >
// 2D
auto pt2d1 = AcGePoint2d(4, 1);
auto pt2d2 = AcGePoint2d(-1, 4);
pt2d1.distanceTo(pt2d2);
// -> 5.83095
getMidpoint2d(pt2d1, pt2d2);
// -> (1.5, 2.5)

// 3D
auto pt3d1 = AcGePoint3d(-5, 1, 2);
auto pt3d2 = AcGePoint3d(4, -1, -4);
pt3d1.distanceTo(pt3d2);
// -> 11
getMidpoint3d(pt3d1, pt3d2);
// -> (-0.5, 0.0, -1.0)
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