标签:summary his lse mon 投影矩阵 需要 情况 ado etc
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。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;
}
/// <param name="projectionMatrix">投影矩阵</param>
/// <param name="viewMatrix">视点矩阵</param>
/// <param name="projection">列表形式的投影矩阵</param>
/// <param name="view">列表形式的视点矩阵</param>
/// <param name="p">要投影的点的引用</param>
/// <param name="pl">要投影的点引用列表</param>
/// <param name="width">屏幕宽</param>
/// <param name="height">屏幕高</param>
/// <param name="rowBase">列表是否以行优先进行矩阵元素的存储</param>
/// <param name="flipLeftToRight">水平翻转</param>
/// <param name="flipUpsideDown">上下翻转</param>
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<float> projection,
IReadOnlyList<float> 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<float> projection,
IReadOnlyList<float> 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<Vector3> pl
)
{
Matrix4x4 PV = projectionMatrix * viewMatrix;
for (int i = 0; i < pl.Count; i++)
{
pl[i] = PV.inverse.MultiplyPoint(pl[i]);
}
}
public void UnProjectScreenToWorld(
IReadOnlyList<float> projection,
IReadOnlyList<float> view,
ref List<Vector3> 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]);
}
}
/// <summary>
/// 获得相机的世界坐标,遵从 Direct3D 标准的左手笛卡尔坐标系。
/// </summary>
/// <param name="viewMatrix">视点矩阵</param>
/// <returns></returns>
public Vector3 GetCameraPosition(Matrix4x4 viewMatrix)
{
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m30, invV.m31, invV.m32);
}
/// <summary>
/// 获得相机的世界坐标,遵从 Direct3D 标准的左手笛卡尔坐标系。
/// </summary>
/// <param name="view">视点矩阵元素列表</param>
/// <param name="rowBase">列表是否以行优先进行矩阵元素的存储</param>
/// <returns></returns>
public Vector3 GetCameraPosition(IReadOnlyList<float> view, bool rowBase = true)
{
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m30, invV.m31, invV.m32);
}
/// <summary>
/// 获得相机的视线方向,遵从 Direct3D 标准的左手笛卡尔坐标系。
/// </summary>
/// <param name="viewMatrix">视点矩阵</param>
/// <returns></returns>
public Vector3 GetCameraViewDirection(Matrix4x4 viewMatrix)
{
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m20, invV.m21, invV.m22);
}
/// <summary>
/// 获得相机的视线方向,遵从 Direct3D 标准的左手笛卡尔坐标系。
/// </summary>
/// <param name="view">视点矩阵元素列表</param>
/// <param name="rowBase">列表是否以行优先进行矩阵元素的存储</param>
/// <returns></returns>
public Vector3 GetCameraViewDirection(IReadOnlyList<float> view, bool rowBase = true)
{
Matrix4x4 viewMatrix = ConstructMatirx(view, rowBase);
Matrix4x4 invV = viewMatrix.inverse;
return new Vector3(invV.m20, invV.m21, invV.m22);
}
/// <summary>
/// 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
/// </summary>
/// <param name="screen">屏幕宽或高</param>
/// <param name="p">像素坐标(指定宽则为横坐标,指定高则为纵坐标)</param>
/// <param name="flip">是否翻转(Unity通常情况下会将纵坐标翻转)</param>
/// <returns></returns>
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<Vector3> pl, float width, float height, bool flipLeftToRight = false, bool flipUpSideDown = false)
{
for(int i = 0; i<pl.Count; 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);
}
}
/// <summary>
/// 从列表中构造Matirx4x4矩阵
/// </summary>
/// <param name="elements">矩阵元素列表</param>
/// <param name="rowBase">列表是否以行优先进行矩阵元素的存储</param>
/// <returns></returns>
public Matrix4x4 ConstructMatirx(IReadOnlyList<float> 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。
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
标签:summary his lse mon 投影矩阵 需要 情况 ado etc
原文地址:https://blog.51cto.com/myselfdream/2494850