因为要做AR的标记功能，所以就要用到坐标的转换，就总结了一下屏幕坐标、世界坐标、相机坐标之间的转换。
首先说明的是Unity3D遵从Direct3D标准的左手笛卡尔坐标系变换规则。
也就是说：
世界坐标系就是左手笛卡尔坐标系(x,y,z),相机也是左手笛卡尔坐标系(u,v,w)，且面向自身坐标系w坐标轴正上方，屏幕以中央为原点，右和上分别为x,y的正方向。
我将工具代码直接上：
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class CameraTransformationUtilities : MonoBehaviour
{
public static CameraTransformationUtilities Instance { get; private set; }
protected CameraTransformationUtilities() { }
private void Start()
{
Instance = this;
}
/// 投影矩阵
/// 视点矩阵
/// 列表形式的投影矩阵
/// 列表形式的视点矩阵
/// 要投影的点的引用
/// 要投影的点引用列表
/// 屏幕宽
/// 屏幕高
/// 列表是否以行优先进行矩阵元素的存储
/// 水平翻转
/// 上下翻转
public void UnprojectScreenToWorld(
Matrix4x4 projectionMatrix,
Matrix4x4 viewMatrix,
ref Vector3 p)
{
// 世界坐标->相机坐标， 相机坐标->屏幕坐标 分别需要 viewMatrix和projectionMatrix
Matrix4x4 PV = projectionMatrix * viewMatrix;
// 逆矩阵即为从屏幕到世界的坐标变换，需指定像素深度
p = PV.inverse.MultiplyPoint(p);
}
public void UnprojectScreenToWorld(
IReadOnlyList projection,
IReadOnlyList view,
ref Vector3 p,
bool rowBase = true
)
{
Matrix4x4 projectionMatrix = ConstructMatirx(projection, rowBase);
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
UnprojectScreenToWorld(projectionMatrix, viewMatrix, ref p);
}
public void UnprojectScreenToWorld(
IReadOnlyList projection,
IReadOnlyList view,
ref Vector3 p,
float width,
float height,
bool rowBase = true,
bool flipLeftToRight = false,
bool flipUpsideDown = false
)
{
Matrix4x4 projectionMatrix = ConstructMatirx(projection, rowBase);
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
ScreenSpaceTransform(ref p, width, height, flipLeftToRight, flipUpsideDown);
UnprojectScreenToWorld(projectionMatrix, viewMatrix, ref p);
}
public void UnProjectScreenToWorld(
Matrix4x4 projectionMatrix,
Matrix4x4 viewMatrix,
ref List pl
)
{
Matrix4x4 PV = projectionMatrix * viewMatrix;
for (int i = 0; i < pl.Count; i++)
{
pl[i] = PV.inverse.MultiplyPoint(pl[i]);
}
}
public void UnProjectScreenToWorld(
IReadOnlyList projection,
IReadOnlyList view,
ref List pl,
float width,
float height,
bool rowBase = true,
bool flipLeftToRight = false,
bool flipUpsideDown = false
)
{
Matrix4x4 projectionMatrix = ConstructMatirx(projection, rowBase);
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
Matrix4x4 PV = projectionMatrix * viewMatrix;
ScreenSpaceTransform(ref pl, width, height, flipLeftToRight, flipUpsideDown);
for(int i = 0; i < pl.Count; i++)
{
pl[i] = PV.inverse.MultiplyPoint(pl[i]);
}
}
///
/// 获得相机的世界坐标，遵从 Direct3D 标准的左手笛卡尔坐标系。
///
/// 视点矩阵
///
public Vector3 GetCameraPosition(Matrix4x4 viewMatrix)
{
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m30, invV.m31, invV.m32);
}
///
/// 获得相机的世界坐标，遵从 Direct3D 标准的左手笛卡尔坐标系。
///
/// 视点矩阵元素列表
/// 列表是否以行优先进行矩阵元素的存储
///
public Vector3 GetCameraPosition(IReadOnlyList view, bool rowBase = true)
{
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m30, invV.m31, invV.m32);
}
///
/// 获得相机的视线方向，遵从 Direct3D 标准的左手笛卡尔坐标系。
///
/// 视点矩阵
///
public Vector3 GetCameraViewDirection(Matrix4x4 viewMatrix)
{
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m20, invV.m21, invV.m22);
}
///
/// 获得相机的视线方向，遵从 Direct3D 标准的左手笛卡尔坐标系。
///
/// 视点矩阵元素列表
/// 列表是否以行优先进行矩阵元素的存储
///
public Vector3 GetCameraViewDirection(IReadOnlyList view, bool rowBase = true)
{
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m20, invV.m21, invV.m22);
}
///
/// 将屏幕点坐标转换成以屏幕中心为原点，
/// 右和上分别为x,y正方向，
/// -1到1的坐标
///
/// 屏幕宽或高
/// 像素坐标(指定宽则为横坐标，指定高则为纵坐标)
/// 是否翻转(Unity通常情况下会将纵坐标翻转)
///
public void ScreenSpaceTransform(ref Vector3 p, float width, float height, bool flipLeftToRight = false, bool flipUpSideDown = false)
{
p.Set((p.x / width * 2 - 1) * (flipLeftToRight ? -1 : 1),
(p.y / height * 2 - 1) * (flipUpSideDown ? -1 : 1),
p.z);
}
public void ScreenSpaceTransform(ref List pl, float width, float height, bool flipLeftToRight = false, bool flipUpSideDown = false)
{
for(int i = 0; i
{
pl[i].Set((pl[i].x / width * 2 - 1) * (flipLeftToRight ? -1 : 1),
(pl[i].y / height * 2 - 1) * (flipUpSideDown ? -1 : 1),
pl[i].z);
}
}
///
/// 从列表中构造Matirx4x4矩阵
///
/// 矩阵元素列表
/// 列表是否以行优先进行矩阵元素的存储
///
public Matrix4x4 ConstructMatirx(IReadOnlyList elements, bool rowBase = true)
{
if (elements.Count != 16) return Matrix4x4.identity;
Matrix4x4 mat = new Matrix4x4();
if (rowBase)
{
mat.m00 = elements[0];
mat.m01 = elements[1];
mat.m02 = elements[2];
mat.m03 = elements[3];
mat.m10 = elements[4];
mat.m11 = elements[5];
mat.m12 = elements[6];
mat.m13 = elements[7];
mat.m20 = elements[8];
mat.m21 = elements[9];
mat.m22 = elements[10];
mat.m23 = elements[11];
mat.m30 = elements[12];
mat.m31 = elements[13];
mat.m32 = elements[14];
mat.m33 = elements[15];
}
else
{
mat.m00 = elements[0];
mat.m10 = elements[1];
mat.m20 = elements[2];
mat.m30 = elements[3];
mat.m01 = elements[4];
mat.m11 = elements[5];
mat.m21 = elements[6];
mat.m31 = elements[7];
mat.m02 = elements[8];
mat.m12 = elements[9];
mat.m22 = elements[10];
mat.m32 = elements[11];
mat.m03 = elements[12];
mat.m11 = elements[13];
mat.m23 = elements[14];
mat.m33 = elements[15];
}
return mat;
}
}
坐标的转换，用的地方特别多，尤其是屏幕划线展示在世界坐标中，我把他形成了工具，直接可以用。
unity 坐标系转换_Unity3D之笛卡尔坐标系转换——屏幕坐标转换世界坐标 世界坐标转换相机坐标工具...
