簡單地說，我有：查找線段矩形交點
這是在視口座標系中，+ X是正確的，+ Y在屏幕上。
而且我需要一個函數，它接受這些參數，並返回矩形邊（矩形中心（0.5,0.5）和點（a，b））之間的直線相交的點。
我知道如何用給定的座標在紙上做到這一點，但是當它涉及到代碼時我無法弄清楚。此外，我意識到這樣的問題已經在不同的線程中得到了解決 - 但我無法在任何地方找到簡單的輸入來輸出函數。
我在Unity3D引擎中這麼做，所以最好在Javascript中，但任何語言或僞代碼將是一個很大的幫助，因爲我可以手工轉換它。
編輯 爲了澄清，我正在尋找類似：
function IntersectFromViewportCenter(x : float, y : float) {
...
return Point(x1, y1);
}
其中（x，y）是圓和（X1，Y1）之外的點的交點。
謝謝
將所有系統都移到以點（0,0）爲中心。計算從原點到（移位）點（x'，y'）與框（-1，-1） - （1,1）的射線交點。縮放並移回。我沒有考慮盒子內部的小事（是否需要？）
x = x - 0.5
y = y - 0.5
if Abs(x) >= Abs(y) then //vertical box edge
y1 = y/x //care with case both y and x = 0
x1 = Sign(x) //+-1
else // horizontal edge
x1 = x/y
y1 = Sign(y)
x1 = 0.5*x1 + 0.5
y1 = 0.5*y1 + 0.5
MBo有正確的想法。這是一種在Unity中實現的方法。我認爲UnityScript不值得使用 - 特別是它不支持擴展方法 - 所以你應該切換語言。 （另外，團結實際上是未命名Unity3D。）
該腳本可以去任何地方在項目：
using UnityEngine;
public static class UnityEngineExtensions {
public static Vector2 Abs(this Vector2 vector) {
for (int i = 0; i < 2; ++i) vector[i] = Mathf.Abs(vector[i]);
return vector;
}
public static Vector2 DividedBy(this Vector2 vector, Vector2 divisor) {
for (int i = 0; i < 2; ++i) vector[i] /= divisor[i];
return vector;
}
public static Vector2 Max(this Rect rect) {
return new Vector2(rect.xMax, rect.yMax);
}
public static Vector2 IntersectionWithRayFromCenter(this Rect rect, Vector2 pointOnRay) {
Vector2 pointOnRay_local = pointOnRay - rect.center;
Vector2 edgeToRayRatios = (rect.Max() - rect.center).DividedBy(pointOnRay_local.Abs());
return (edgeToRayRatios.x < edgeToRayRatios.y) ?
new Vector2(pointOnRay_local.x > 0 ? rect.xMax : rect.xMin,
pointOnRay_local.y * edgeToRayRatios.x + rect.center.y) :
new Vector2(pointOnRay_local.x * edgeToRayRatios.y + rect.center.x,
pointOnRay_local.y > 0 ? rect.yMax : rect.yMin);
}
}
裝上此腳本等的遊戲對象，並在檢查設置它的變量。
#pragma warning disable 0649
using System;
using UnityEngine;
public class VisualizeRectIntersectionWithRayFromCenter : MonoBehaviour {
[SerializeField] Rect rect;
[SerializeField] Vector2 point;
[Serializable] class Colors {
public Color rect, point, intersection;
} [SerializeField] Colors colors;
void OnDrawGizmos() {
Gizmos.color = colors.rect;
Vector2[] corners = {new Vector2(rect.xMin, rect.yMin), new Vector2(rect.xMin, rect.yMax),
rect.Max(), new Vector2(rect.xMax, rect.yMin)};
int i = 0;
while (i < 3) Gizmos.DrawLine(corners[i], corners[++i]);
Gizmos.DrawLine(corners[3], corners[0]);
Gizmos.color = colors.point;
Gizmos.DrawLine(rect.center, point);
Gizmos.color = colors.intersection;
Gizmos.DrawLine(rect.center, rect.IntersectionWithRayFromCenter(pointOnRay: point));
}
}
bool LineRectIntersection(Vector2 lineStartPoint, Vector2 lineEndPoint, Rect rectangle, ref double resultX, ref double resultY)
{
Vector2 minXLinePoint = (lineStartPoint.x <= lineEndPoint.x) ? (lineStartPoint) : (lineEndPoint);
Vector2 maxXLinePoint = (lineStartPoint.x <= lineEndPoint.x) ? (lineEndPoint) : (lineStartPoint);
Vector2 minYLinePoint = (lineStartPoint.y <= lineEndPoint.y) ? (lineStartPoint) : (lineEndPoint);
Vector2 maxYLinePoint = (lineStartPoint.y <= lineEndPoint.y) ? (lineEndPoint) : (lineStartPoint);
double rectMaxX = rectangle.xMax;
double rectMinX = rectangle.xMin;
double rectMaxY = rectangle.yMax;
double rectMinY = rectangle.yMin;
if (minXLinePoint.x <= rectMaxX && rectMaxX <= maxXLinePoint.x)
{
double m = (maxXLinePoint.y - minXLinePoint.y)/(maxXLinePoint.x - minXLinePoint.x);
double intersectionY = ((rectMaxX - ((double)minXLinePoint.x)) * m) + ((double)minXLinePoint.y);
if(minYLinePoint.y <= intersectionY && intersectionY <= maxYLinePoint.y)
{
resultX = rectMaxX;
resultY = intersectionY;
return true;
}
}
if (minXLinePoint.x <= rectMinX && rectMinX <= maxXLinePoint.x)
{
double m = (maxXLinePoint.y - minXLinePoint.y)/(maxXLinePoint.x - minXLinePoint.x);
double intersectionY = ((rectMinX - ((double)minXLinePoint.x)) * m) + ((double)minXLinePoint.y);
if (minYLinePoint.y <= intersectionY && intersectionY <= maxYLinePoint.y)
{
resultX = rectMinX;
resultY = intersectionY;
return true;
}
}
if (minYLinePoint.y <= rectMaxY && rectMaxY <= maxYLinePoint.y)
{
double rm = (maxYLinePoint.x - minYLinePoint.x)/(maxYLinePoint.y - minYLinePoint.y);
double intersectionX = ((rectMaxY - ((double)minYLinePoint.y)) * rm) + ((double)minYLinePoint.x);
if (minXLinePoint.x <= intersectionX && intersectionX <= maxXLinePoint.x)
{
resultX = intersectionX;
resultY = rectMaxY;
return true;
}
}
if (minYLinePoint.y <= rectMinY && rectMinY <= maxYLinePoint.y)
{
double rm = (maxYLinePoint.x - minYLinePoint.x)/(maxYLinePoint.y - minYLinePoint.y);
double intersectionX = ((rectMinY - ((double)minYLinePoint.y)) * rm) + ((double)minYLinePoint.x);
if (minXLinePoint.x <= intersectionX && intersectionX <= maxXLinePoint.x)
{
resultX = intersectionX;
resultY = rectMinY;
return true;
}
}
return false;
}
@chakmeshma，您的解決方案几乎是正確的，但你也必須檢查交點是否在矩形內，以避免邊界情況：
private static bool LineRectIntersection(Vector2 lineStartPoint, Vector2 lineEndPoint, Rect rectangle, ref Vector2 result)
{
Vector2 minXLinePoint = lineStartPoint.x <= lineEndPoint.x ? lineStartPoint : lineEndPoint;
Vector2 maxXLinePoint = lineStartPoint.x <= lineEndPoint.x ? lineEndPoint : lineStartPoint;
Vector2 minYLinePoint = lineStartPoint.y <= lineEndPoint.y ? lineStartPoint : lineEndPoint;
Vector2 maxYLinePoint = lineStartPoint.y <= lineEndPoint.y ? lineEndPoint : lineStartPoint;
double rectMaxX = rectangle.xMax;
double rectMinX = rectangle.xMin;
double rectMaxY = rectangle.yMax;
double rectMinY = rectangle.yMin;
if (minXLinePoint.x <= rectMaxX && rectMaxX <= maxXLinePoint.x)
{
double m = (maxXLinePoint.y - minXLinePoint.y)/(maxXLinePoint.x - minXLinePoint.x);
double intersectionY = ((rectMaxX - minXLinePoint.x) * m) + minXLinePoint.y;
if (minYLinePoint.y <= intersectionY && intersectionY <= maxYLinePoint.y
&& rectMinY <= intersectionY && intersectionY <= rectMaxY)
{
result = new Vector2((float)rectMaxX, (float)intersectionY);
return true;
}
}
if (minXLinePoint.x <= rectMinX && rectMinX <= maxXLinePoint.x)
{
double m = (maxXLinePoint.y - minXLinePoint.y)/(maxXLinePoint.x - minXLinePoint.x);
double intersectionY = ((rectMinX - minXLinePoint.x) * m) + minXLinePoint.y;
if (minYLinePoint.y <= intersectionY && intersectionY <= maxYLinePoint.y
&& rectMinY <= intersectionY && intersectionY <= rectMaxY)
{
result = new Vector2((float)rectMinX, (float)intersectionY);
return true;
}
}
if (minYLinePoint.y <= rectMaxY && rectMaxY <= maxYLinePoint.y)
{
double rm = (maxYLinePoint.x - minYLinePoint.x)/(maxYLinePoint.y - minYLinePoint.y);
double intersectionX = ((rectMaxY - minYLinePoint.y) * rm) + minYLinePoint.x;
if (minXLinePoint.x <= intersectionX && intersectionX <= maxXLinePoint.x
&& rectMinX <= intersectionX && intersectionX <= rectMaxX)
{
result = new Vector2((float)intersectionX, (float)rectMaxY);
return true;
}
}
if (minYLinePoint.y <= rectMinY && rectMinY <= maxYLinePoint.y)
{
double rm = (maxYLinePoint.x - minYLinePoint.x)/(maxYLinePoint.y - minYLinePoint.y);
double intersectionX = ((rectMinY - minYLinePoint.y) * rm) + minYLinePoint.x;
if (minXLinePoint.x <= intersectionX && intersectionX <= maxXLinePoint.x
&& rectMinX <= intersectionX && intersectionX <= rectMaxX)
{
result = new Vector2((float)intersectionX, (float)rectMinY);
return true;
}
}
return false;
}
}
謝謝，這似乎爲工作我。我不得不添加一個快速修復，使其在屏幕的底部和左側工作，但這可能是因爲我在3D世界空間中進行的轉換事先翻轉了座標。 – jt78
邊緣上的點的乘法/加法是不必要的。 – Jessy