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CJKmkp
2025-08-23 21:39:21 +08:00
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commit f67b4db4ba
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InkCanvasForClassX/Libraries/Vector.cs
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using System;
namespace InkCanvasForClassX.Libraries
{
/// <summary>
/// 提供了對平面向量的坐標運算
/// </summary>
public class Vector {
private double _x = 0;
private double _y = 0;
public Vector(double x = 0, double y = 0) {
_x = x;
_y = y;
}
public double X {
get => _x;
set => _x = value;
}
public double Y {
get => _y;
set => _y = value;
}
/// <summary>
/// 將該向量改變為其相反向量
/// </summary>
public Vector Negate() {
_x = -_x;
_y = -_y;
return this;
}
/// <summary>
/// 提供一個<c>Vector</c>，返回該<c>Vector</c>的相反向量
/// </summary>
public static Vector NegateVector(Vector vec) {
return new Vector(-vec.X, -vec.Y);
}
/// <summary>
/// Csharp中的<c>Math.Hypot</c>實現
/// </summary>
private static double Hypot(params double[] values)
{
double sum = 0;
foreach (var value in values) {
sum += Math.Pow(value, 2);
}
return Math.Sqrt(sum);
}
/// <summary>
/// 獲取該向量的長度
/// </summary>
public double Length => Vector.Hypot(_x,_y);
/// <summary>
/// 獲取該向量的未開平方的長度
/// </summary>
public double LengthSquared => _x * _x + _y * _y;
/// <summary>
/// 將該向量和另一個向量相加
/// </summary>
public Vector Add(Vector vec)
{
_x = _x + vec.X;
_y = _y + vec.Y;
return this;
}
/// <summary>
/// 提供兩個<c>Vector</c>，返回相加後的<c>Vector</c>
/// </summary>
public static Vector AddVectors(Vector vec1, Vector vec2)
{
return new Vector(vec1.X + vec2.X, vec1.Y + vec2.Y);
}
/// <summary>
/// 將該向量減去另一個向量
/// </summary>
public Vector Subtract(Vector vec)
{
_x = _x - vec.X;
_y = _y - vec.Y;
return this;
}
/// <summary>
/// 提供兩個<c>Vector</c>，返回<c><paramref name="vec1"/>-<paramref name="vec2"/></c>後的<c>Vector</c>
/// </summary>
public static Vector SubtractVectors(Vector vec1, Vector vec2)
{
return new Vector(vec1.X - vec2.X, vec1.Y - vec2.Y);
}
/// <summary>
/// 將該向量除以一個數值
/// </summary>
public Vector DivideBy(double n)
{
_x = _x / n;
_y = _y / n;
return this;
}
/// <summary>
/// 提供兩個<c>Vector</c>，返回<c><paramref name="vec"/>/<paramref name="n"/></c>後的<c>Vector</c>
/// </summary>
public static Vector DivideByVector(Vector vec, double n)
{
return new Vector(vec.X / n, vec.Y / n);
}
/// <summary>
/// 將該向量乘以一個數值
/// </summary>
public Vector Multiply(double n)
{
_x = _x * n;
_y = _y * n;
return this;
}
/// <summary>
/// 提供兩個<c>Vector</c>，返回<c><paramref name="vec"/>*<paramref name="n"/></c>後的<c>Vector</c>
/// </summary>
public static Vector MultiplyVector(Vector vec, double n)
{
return new Vector(vec.X * n, vec.Y * n);
}
/// <summary>
/// 將該向量垂直旋轉
/// </summary>
public Vector PerpendicularRotation() {
var _t = _x;
_x = _y;
_y = - _t;
return this;
}
/// <summary>
/// 提供<c>Vector</c>，返回垂直旋轉後的<c>Vector</c>
/// </summary>
public static Vector PerpendicularRotationVector(Vector vec)
{
return new Vector(vec.Y, - vec.X);
}
/// <summary>
/// 提供兩個<c>Vector</c>，返回兩個<c>Vector</c>點乘後的数值
/// </summary>
public static double DotVectors(Vector vec1, Vector vec2)
{
return vec1.X * vec2.X + vec1.Y * vec2.Y;
}
/// <summary>
/// 判斷該向量和另外一個向量是否相等
/// </summary>
public bool IsEqual(Vector vec)
{
return Math.Abs(_x - vec.X) < 0.01 && Math.Abs(_y - vec.Y) < 0.01;
}
/// <summary>
/// 獲取該向量和另一個向量的平方距離
/// </summary>
public double DistLengthSquared(Vector vec) {
var subVec = Vector.SubtractVectors(this, vec);
return subVec.LengthSquared;
}
/// <summary>
/// 獲取一個向量和另一個向量的平方距離
/// </summary>
public static double DistLengthSquaredVectors(Vector vec1, Vector vec2)
{
var subVec = Vector.SubtractVectors(vec1, vec2);
return subVec.LengthSquared;
}
/// <summary>
/// 獲取該向量和另一個向量的距離
/// </summary>
public double DistLength(Vector vec) {
return Vector.Hypot(this._y - vec.Y, this._x - vec.X);
}
/// <summary>
/// 獲取一個向量和另一個向量的距離
/// </summary>
public static double DistLengthVectors(Vector vec1, Vector vec2)
{
return Vector.Hypot(vec1.Y - vec2.Y, vec1.X - vec2.X);
}
/// <summary>
/// 將該向量修改為其中間向量
/// </summary>
public Vector Med(Vector vec) {
var addVec = new Vector(_x, _y).Add(vec);
addVec.Multiply(0.5);
_x = addVec.X;
_y = addVec.Y;
return this;
}
/// <summary>
/// 獲取一個向量和另一個向量的中間向量
/// </summary>
public static Vector MedVectors(Vector vec1, Vector vec2) {
var addVec = Vector.AddVectors(vec1, vec2);
return addVec.Multiply(0.5);
}
/// <summary>
/// 將該向量圍繞另一個向量旋轉r弧度
/// </summary>
public Vector Rotate(Vector vec, double r) {
var sin = Math.Sin(r);
var cos = Math.Cos(r);
var px = _x - vec.X;
var py = _y - vec.Y;
var nx = px * cos - py * sin;
var ny = px * sin + py * cos;
_x = nx + vec.X;
_y = ny + vec.Y;
return this;
}
/// <summary>
/// 將一個向量圍繞另一個向量旋轉r弧度
/// </summary>
public static Vector RotateVectors(Vector vec1, Vector vec2, double r)
{
var sin = Math.Sin(r);
var cos = Math.Cos(r);
var px = vec1.X - vec2.X;
var py = vec1.Y - vec2.Y;
var nx = px * cos - py * sin;
var ny = px * sin + py * cos;
return new Vector(nx + vec2.X, ny + vec2.Y);
}
/// <summary>
/// 將該向量與另一個向量插值
/// </summary>
public Vector Interpolate(Vector vec, double t) {
Add(SubtractVectors(vec, this).Multiply(t));
return this;
}
/// <summary>
/// 將一個向量與另一個向量插值
/// </summary>
public static Vector InterpolateVectors(Vector vec1, Vector vec2, double t) {
return AddVectors(vec1, SubtractVectors(vec2, vec1).Multiply(t));
}
/// <summary>
/// 將該向量投影在向量<paramref name="vec"/>的方向上，並附加距離<paramref name="c"/>
/// </summary>
public Vector Project(Vector vec, double c) {
Add(vec.Multiply(c));
return this;
}
/// <summary>
/// 將<paramref name="vec1"/>投影在向量<paramref name="vec2"/>的方向上，並附加距離<paramref name="c"/>
/// </summary>
public static Vector ProjectVectors(Vector vec1, Vector vec2, double c) {
return AddVectors(vec1, MultiplyVector(vec2,c));
}
/// <summary>
/// 取得單位向量
/// </summary>
public Vector Unit()
{
return DivideByVector(this, Length);
}
/// <summary>
/// 取得單位向量
/// </summary>
public static Vector UnitVector(Vector vec)
{
return DivideByVector(vec, vec.Length);
}
}
}