私は5歳のように誰かにこれを説明できることを望んでいます。何時間もこれに苦労してきたし、私が間違っていることを理解できないからです。
Camera
2.5Dゲームのクラスを作成しました。意図は、次のようなワールドおよびスクリーンスペースをサポートすることです。
カメラは右側の黒いものです。その画像では、+ Z軸は上向きで、-Zは下向きです。ご覧のとおり、ワールド空間と画面空間の両方の左上に(0、0)があります。
カメラが期待どおりに動作していることを証明するために、いくつかの単体テストを書き始めました。私のテストでは、ワールド、ビュー、およびスクリーンスペースで座標をプロットします。最終的には、イメージ比較を使用してそれらが正しいことを断言しますが、今のところ、テストでは結果を表示するだけです。
レンダリングロジックはCamera.ViewMatrix
、ワールド空間を表示空間Camera.WorldPointToScreen
に変換し、ワールド空間を画面空間に変換するために使用します。
テストの例を次に示します。
[Fact]
public void foo()
{
var camera = new Camera(new Viewport(0, 0, 250, 100));
DrawingVisual worldRender;
DrawingVisual viewRender;
DrawingVisual screenRender;
this.Render(camera, out worldRender, out viewRender, out screenRender, new Vector3(30, 0, 0), new Vector3(30, 40, 0));
this.ShowRenders(camera, worldRender, viewRender, screenRender);
}
このテストを実行すると、次のように表示されます。
ワールド空間は問題ないように見えますが、z軸は視聴者に向かうのではなく画面に入ると思われます。
ビュースペースは私を完全に困惑させます。カメラが(0、0)の上に座って、シーンの中心に向かっていることを期待していました。代わりに、z軸は間違った方向にあり、カメラは予想とは反対の角に配置されています!
画面スペースはまったく別のものになると思いますが、Camera
クラスで私が間違っていることを誰かが説明できますか?
更新
私は物事を期待どおりに視覚的に見えるようにするという点でいくつかの進歩を遂げましたが、それは直感を通してのみでした。どんな啓発も大歓迎です。
ビュースペースが予想と比べて垂直と水平の両方に反転していることに気づいたので、それに応じてビューマトリックスをスケーリングして変更しました。
this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) *
Matrix.CreateScale(this.zoom, this.zoom, 1) *
Matrix.CreateScale(-1, -1, 1);
2つのCreateScale
呼び出しを組み合わせることができますが、明確にするために別々に残しました。繰り返しになりますが、なぜこれが必要なのかわかりませんが、ビュースペースが修正されました。
しかし、今では画面スペースを垂直に反転する必要があるため、それに応じて投影マトリックスを変更しました。
this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2)
* Matrix.CreateScale(1, -1, 1);
そして、これは私が最初の試みから期待していたものになります:
またCamera
、a SpriteBatch
を介してスプライトをレンダリングするために使用してみましたが、すべてがそこで動作することを確認しました。
しかし、疑問は残ります。なぜ空間座標を期待どおりに取得するために、この軸のすべての反転を行う必要があるのですか?
更新2
その後、テストスイートのレンダリングロジックを改善して、ジオメトリをサポートし、カメラから離れるにつれてラインが明るくなるようにしました。目の錯覚を避け、自分が自分だと思っているものを見ていることを自分自身にさらに証明するために、これをしたかったのです。
以下に例を示します。
この場合、3つのジオメトリがあります。キューブ、球、およびキューブの上面のポリラインです。線を暗くしたり明るくしたりすると、カメラに近いジオメトリの部分が正しく識別されることに注意してください。
私が入れなければならなかった負のスケーリングを削除すると、私は見ます:
だから、あなたは私がまだ同じ船に乗っているのを見ることができます-物事を正しく表示するために、私はまだ私の行列にそれらの垂直と水平のフリップが必要です。
人々に遊ぶための再現を提供するために、上記を生成するために必要な完全なコードを以下に示します。テストハーネス経由で実行する場合は、xunitパッケージをインストールするだけです。
Camera.cs:
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Graphics;
using System.Diagnostics;
public sealed class Camera
{
private readonly Viewport viewport;
private readonly Matrix projectionMatrix;
private Matrix? viewMatrix;
private Vector3 location;
private Vector3 target;
private Vector3 up;
private float zoom;
public Camera(Viewport viewport)
{
this.viewport = viewport;
// for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/
this.projectionMatrix = Matrix.CreatePerspectiveFieldOfView(0.7853982f, viewport.AspectRatio, 1, 2)
* Matrix.CreateScale(1, -1, 1);
// defaults
this.location = new Vector3(this.viewport.Width / 2, this.viewport.Height, 100);
this.target = new Vector3(this.viewport.Width / 2, this.viewport.Height / 2, 0);
this.up = new Vector3(0, 0, 1);
this.zoom = 1;
}
public Viewport Viewport
{
get { return this.viewport; }
}
public Vector3 Location
{
get { return this.location; }
set
{
this.location = value;
this.viewMatrix = null;
}
}
public Vector3 Target
{
get { return this.target; }
set
{
this.target = value;
this.viewMatrix = null;
}
}
public Vector3 Up
{
get { return this.up; }
set
{
this.up = value;
this.viewMatrix = null;
}
}
public float Zoom
{
get { return this.zoom; }
set
{
this.zoom = value;
this.viewMatrix = null;
}
}
public Matrix ProjectionMatrix
{
get { return this.projectionMatrix; }
}
public Matrix ViewMatrix
{
get
{
if (this.viewMatrix == null)
{
// for an explanation of the negative scaling, see: http://gamedev.stackexchange.com/questions/63409/
this.viewMatrix = Matrix.CreateLookAt(this.location, this.target, this.up) *
Matrix.CreateScale(this.zoom) *
Matrix.CreateScale(-1, -1, 1);
}
return this.viewMatrix.Value;
}
}
public Vector2 WorldPointToScreen(Vector3 point)
{
var result = viewport.Project(point, this.ProjectionMatrix, this.ViewMatrix, Matrix.Identity);
return new Vector2(result.X, result.Y);
}
public void WorldPointsToScreen(Vector3[] points, Vector2[] destination)
{
Debug.Assert(points != null);
Debug.Assert(destination != null);
Debug.Assert(points.Length == destination.Length);
for (var i = 0; i < points.Length; ++i)
{
destination[i] = this.WorldPointToScreen(points[i]);
}
}
}
CameraFixture.cs:
using Microsoft.Xna.Framework.Graphics;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Media;
using Xunit;
using XNA = Microsoft.Xna.Framework;
public sealed class CameraFixture
{
[Fact]
public void foo()
{
var camera = new Camera(new Viewport(0, 0, 250, 100));
DrawingVisual worldRender;
DrawingVisual viewRender;
DrawingVisual screenRender;
this.Render(
camera,
out worldRender,
out viewRender,
out screenRender,
new Sphere(30, 15) { WorldMatrix = XNA.Matrix.CreateTranslation(155, 50, 0) },
new Cube(30) { WorldMatrix = XNA.Matrix.CreateTranslation(75, 60, 15) },
new PolyLine(new XNA.Vector3(0, 0, 0), new XNA.Vector3(10, 10, 0), new XNA.Vector3(20, 0, 0), new XNA.Vector3(0, 0, 0)) { WorldMatrix = XNA.Matrix.CreateTranslation(65, 55, 30) });
this.ShowRenders(worldRender, viewRender, screenRender);
}
#region Supporting Fields
private static readonly Pen xAxisPen = new Pen(Brushes.Red, 2);
private static readonly Pen yAxisPen = new Pen(Brushes.Green, 2);
private static readonly Pen zAxisPen = new Pen(Brushes.Blue, 2);
private static readonly Pen viewportPen = new Pen(Brushes.Gray, 1);
private static readonly Pen nonScreenSpacePen = new Pen(Brushes.Black, 0.5);
private static readonly Color geometryBaseColor = Colors.Black;
#endregion
#region Supporting Methods
private void Render(Camera camera, out DrawingVisual worldRender, out DrawingVisual viewRender, out DrawingVisual screenRender, params Geometry[] geometries)
{
var worldDrawingVisual = new DrawingVisual();
var viewDrawingVisual = new DrawingVisual();
var screenDrawingVisual = new DrawingVisual();
const int axisLength = 15;
using (var worldDrawingContext = worldDrawingVisual.RenderOpen())
using (var viewDrawingContext = viewDrawingVisual.RenderOpen())
using (var screenDrawingContext = screenDrawingVisual.RenderOpen())
{
// draw lines around the camera's viewport
var viewportBounds = camera.Viewport.Bounds;
var viewportLines = new Tuple<int, int, int, int>[]
{
Tuple.Create(viewportBounds.Left, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Top),
Tuple.Create(viewportBounds.Left, viewportBounds.Top, viewportBounds.Right, viewportBounds.Top),
Tuple.Create(viewportBounds.Right, viewportBounds.Top, viewportBounds.Right, viewportBounds.Bottom),
Tuple.Create(viewportBounds.Right, viewportBounds.Bottom, viewportBounds.Left, viewportBounds.Bottom)
};
foreach (var viewportLine in viewportLines)
{
var viewStart = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0), camera.ViewMatrix);
var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0), camera.ViewMatrix);
var screenStart = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item1, viewportLine.Item2, 0));
var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(viewportLine.Item3, viewportLine.Item4, 0));
worldDrawingContext.DrawLine(viewportPen, new Point(viewportLine.Item1, viewportLine.Item2), new Point(viewportLine.Item3, viewportLine.Item4));
viewDrawingContext.DrawLine(viewportPen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y));
screenDrawingContext.DrawLine(viewportPen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y));
}
// draw axes
var axisLines = new Tuple<int, int, int, int, int, int, Pen>[]
{
Tuple.Create(0, 0, 0, axisLength, 0, 0, xAxisPen),
Tuple.Create(0, 0, 0, 0, axisLength, 0, yAxisPen),
Tuple.Create(0, 0, 0, 0, 0, axisLength, zAxisPen)
};
foreach (var axisLine in axisLines)
{
var viewStart = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3), camera.ViewMatrix);
var viewEnd = XNA.Vector3.Transform(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6), camera.ViewMatrix);
var screenStart = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item1, axisLine.Item2, axisLine.Item3));
var screenEnd = camera.WorldPointToScreen(new XNA.Vector3(axisLine.Item4, axisLine.Item5, axisLine.Item6));
worldDrawingContext.DrawLine(axisLine.Item7, new Point(axisLine.Item1, axisLine.Item2), new Point(axisLine.Item4, axisLine.Item5));
viewDrawingContext.DrawLine(axisLine.Item7, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y));
screenDrawingContext.DrawLine(axisLine.Item7, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y));
}
// for all points in all geometries to be rendered, find the closest and furthest away from the camera so we can lighten lines that are further away
var distancesToAllGeometrySections = from geometry in geometries
let geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix
from section in geometry.Sections
from point in new XNA.Vector3[] { section.Item1, section.Item2 }
let viewPoint = XNA.Vector3.Transform(point, geometryViewMatrix)
select viewPoint.Length();
var furthestDistance = distancesToAllGeometrySections.Max();
var closestDistance = distancesToAllGeometrySections.Min();
var deltaDistance = Math.Max(0.000001f, furthestDistance - closestDistance);
// draw each geometry
for (var i = 0; i < geometries.Length; ++i)
{
var geometry = geometries[i];
// there's probably a more correct name for this, but basically this gets the geometry relative to the camera so we can check how far away each point is from the camera
var geometryViewMatrix = geometry.WorldMatrix * camera.ViewMatrix;
// we order roughly by those sections furthest from the camera to those closest, so that the closer ones "overwrite" the ones further away
var orderedSections = from section in geometry.Sections
let startPointRelativeToCamera = XNA.Vector3.Transform(section.Item1, geometryViewMatrix)
let endPointRelativeToCamera = XNA.Vector3.Transform(section.Item2, geometryViewMatrix)
let startPointDistance = startPointRelativeToCamera.Length()
let endPointDistance = endPointRelativeToCamera.Length()
orderby (startPointDistance + endPointDistance) descending
select new { Section = section, DistanceToStart = startPointDistance, DistanceToEnd = endPointDistance };
foreach (var orderedSection in orderedSections)
{
var start = XNA.Vector3.Transform(orderedSection.Section.Item1, geometry.WorldMatrix);
var end = XNA.Vector3.Transform(orderedSection.Section.Item2, geometry.WorldMatrix);
var viewStart = XNA.Vector3.Transform(start, camera.ViewMatrix);
var viewEnd = XNA.Vector3.Transform(end, camera.ViewMatrix);
worldDrawingContext.DrawLine(nonScreenSpacePen, new Point(start.X, start.Y), new Point(end.X, end.Y));
viewDrawingContext.DrawLine(nonScreenSpacePen, new Point(viewStart.X, viewStart.Y), new Point(viewEnd.X, viewEnd.Y));
// screen rendering is more complicated purely because I wanted geometry to fade the further away it is from the camera
// otherwise, it's very hard to tell whether the rendering is actually correct or not
var startDistanceRatio = (orderedSection.DistanceToStart - closestDistance) / deltaDistance;
var endDistanceRatio = (orderedSection.DistanceToEnd - closestDistance) / deltaDistance;
// lerp towards white based on distance from camera, but only to a maximum of 90%
var startColor = Lerp(geometryBaseColor, Colors.White, startDistanceRatio * 0.9f);
var endColor = Lerp(geometryBaseColor, Colors.White, endDistanceRatio * 0.9f);
var screenStart = camera.WorldPointToScreen(start);
var screenEnd = camera.WorldPointToScreen(end);
var brush = new LinearGradientBrush
{
StartPoint = new Point(screenStart.X, screenStart.Y),
EndPoint = new Point(screenEnd.X, screenEnd.Y),
MappingMode = BrushMappingMode.Absolute
};
brush.GradientStops.Add(new GradientStop(startColor, 0));
brush.GradientStops.Add(new GradientStop(endColor, 1));
var pen = new Pen(brush, 1);
brush.Freeze();
pen.Freeze();
screenDrawingContext.DrawLine(pen, new Point(screenStart.X, screenStart.Y), new Point(screenEnd.X, screenEnd.Y));
}
}
}
worldRender = worldDrawingVisual;
viewRender = viewDrawingVisual;
screenRender = screenDrawingVisual;
}
private static float Lerp(float start, float end, float amount)
{
var difference = end - start;
var adjusted = difference * amount;
return start + adjusted;
}
private static Color Lerp(Color color, Color to, float amount)
{
var sr = color.R;
var sg = color.G;
var sb = color.B;
var er = to.R;
var eg = to.G;
var eb = to.B;
var r = (byte)Lerp(sr, er, amount);
var g = (byte)Lerp(sg, eg, amount);
var b = (byte)Lerp(sb, eb, amount);
return Color.FromArgb(255, r, g, b);
}
private void ShowRenders(DrawingVisual worldRender, DrawingVisual viewRender, DrawingVisual screenRender)
{
var itemsControl = new ItemsControl();
itemsControl.Items.Add(new HeaderedContentControl { Header = "World", Content = new DrawingVisualHost(worldRender)});
itemsControl.Items.Add(new HeaderedContentControl { Header = "View", Content = new DrawingVisualHost(viewRender) });
itemsControl.Items.Add(new HeaderedContentControl { Header = "Screen", Content = new DrawingVisualHost(screenRender) });
var window = new Window
{
Title = "Renders",
Content = itemsControl,
ShowInTaskbar = true,
SizeToContent = SizeToContent.WidthAndHeight
};
window.ShowDialog();
}
#endregion
#region Supporting Types
// stupidly simple 3D geometry class, consisting of a series of sections that will be connected by lines
private abstract class Geometry
{
public abstract IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections
{
get;
}
public XNA.Matrix WorldMatrix
{
get;
set;
}
}
private sealed class Line : Geometry
{
private readonly XNA.Vector3 magnitude;
public Line(XNA.Vector3 magnitude)
{
this.magnitude = magnitude;
}
public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections
{
get
{
yield return Tuple.Create(XNA.Vector3.Zero, this.magnitude);
}
}
}
private sealed class PolyLine : Geometry
{
private readonly XNA.Vector3[] points;
public PolyLine(params XNA.Vector3[] points)
{
this.points = points;
}
public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections
{
get
{
if (this.points.Length < 2)
{
yield break;
}
var end = this.points[0];
for (var i = 1; i < this.points.Length; ++i)
{
var start = end;
end = this.points[i];
yield return Tuple.Create(start, end);
}
}
}
}
private sealed class Cube : Geometry
{
private readonly float size;
public Cube(float size)
{
this.size = size;
}
public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections
{
get
{
var halfSize = this.size / 2;
var frontBottomLeft = new XNA.Vector3(-halfSize, halfSize, -halfSize);
var frontBottomRight = new XNA.Vector3(halfSize, halfSize, -halfSize);
var frontTopLeft = new XNA.Vector3(-halfSize, halfSize, halfSize);
var frontTopRight = new XNA.Vector3(halfSize, halfSize, halfSize);
var backBottomLeft = new XNA.Vector3(-halfSize, -halfSize, -halfSize);
var backBottomRight = new XNA.Vector3(halfSize, -halfSize, -halfSize);
var backTopLeft = new XNA.Vector3(-halfSize, -halfSize, halfSize);
var backTopRight = new XNA.Vector3(halfSize, -halfSize, halfSize);
// front face
yield return Tuple.Create(frontBottomLeft, frontBottomRight);
yield return Tuple.Create(frontBottomLeft, frontTopLeft);
yield return Tuple.Create(frontTopLeft, frontTopRight);
yield return Tuple.Create(frontTopRight, frontBottomRight);
// left face
yield return Tuple.Create(frontTopLeft, backTopLeft);
yield return Tuple.Create(backTopLeft, backBottomLeft);
yield return Tuple.Create(backBottomLeft, frontBottomLeft);
// right face
yield return Tuple.Create(frontTopRight, backTopRight);
yield return Tuple.Create(backTopRight, backBottomRight);
yield return Tuple.Create(backBottomRight, frontBottomRight);
// back face
yield return Tuple.Create(backBottomLeft, backBottomRight);
yield return Tuple.Create(backTopLeft, backTopRight);
}
}
}
private sealed class Sphere : Geometry
{
private readonly float radius;
private readonly int subsections;
public Sphere(float radius, int subsections)
{
this.radius = radius;
this.subsections = subsections;
}
public override IEnumerable<Tuple<XNA.Vector3, XNA.Vector3>> Sections
{
get
{
var latitudeLines = this.subsections;
var longitudeLines = this.subsections;
// see http://stackoverflow.com/a/4082020/5380
var results = from latitudeLine in Enumerable.Range(0, latitudeLines)
from longitudeLine in Enumerable.Range(0, longitudeLines)
let latitudeRatio = latitudeLine / (float)latitudeLines
let longitudeRatio = longitudeLine / (float)longitudeLines
let nextLatitudeRatio = (latitudeLine + 1) / (float)latitudeLines
let nextLongitudeRatio = (longitudeLine + 1) / (float)longitudeLines
let z1 = Math.Cos(Math.PI * latitudeRatio)
let z2 = Math.Cos(Math.PI * nextLatitudeRatio)
let x1 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio)
let y1 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio)
let x2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Cos(Math.PI * 2 * longitudeRatio)
let y2 = Math.Sin(Math.PI * nextLatitudeRatio) * Math.Sin(Math.PI * 2 * longitudeRatio)
let x3 = Math.Sin(Math.PI * latitudeRatio) * Math.Cos(Math.PI * 2 * nextLongitudeRatio)
let y3 = Math.Sin(Math.PI * latitudeRatio) * Math.Sin(Math.PI * 2 * nextLongitudeRatio)
let start = new XNA.Vector3((float)x1 * radius, (float)y1 * radius, (float)z1 * radius)
let firstEnd = new XNA.Vector3((float)x2 * radius, (float)y2 * radius, (float)z2 * radius)
let secondEnd = new XNA.Vector3((float)x3 * radius, (float)y3 * radius, (float)z1 * radius)
select new { First = Tuple.Create(start, firstEnd), Second = Tuple.Create(start, secondEnd) };
foreach (var result in results)
{
yield return result.First;
yield return result.Second;
}
}
}
}
#endregion
}
Viewport.Project
。ワールドマトリックスを必要とするという事実を除けば、なぜこれが必要なのかはまだよくわかりません。そのため、APIにワールドマトリックスを追加しました。必要に応じて削除することになるかもしれません。