/// <summary>
/// 屏幕空间插值生成新顶点，此时已近经过透视除法，z信息已经没有作用
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <param name="t"></param>
/// <returns></returns>
public static CVertex ScreenSpaceLerpVertex(CVertex v1, CVertex v2, float t)
{
CVertex v = new CVertex();
float u = MathUntil.Lerp(left.u, right.u, lerpFactor) * w * (_texture.Width - 1);
float v = MathUntil.Lerp(left.v, right.v, lerpFactor) * w * (_texture.Height - 1);
float r = MathUntil.Lerp(left.color.r, right.color.r, lerpFactor) * w * 255;
float g = MathUntil.Lerp(left.color.g, right.color.g, lerpFactor) * w * 255;
float b = MathUntil.Lerp(left.color.b, right.color.b, lerpFactor) * w * 255;
}
public CVertex(CVertex v)
{
point = new CVector3D(v.point.x, v.point.y, v.point.z, 1);
color.r = v.color.r;
color.g = v.color.g;
color.b = v.color.b;
onePerZ = 1;
this.u = v.u;
this.v = v.v;
}
public CVertex(CVertex v)
{
point = new CVector3D(v.point.x, v.point.y, v.point.z, 1);
color.r = v.color.r;
color.g = v.color.g;
color.b = v.color.b;
onePerZ = 1;
this.u = v.u;
this.v = v.v;
}
/// <summary>
/// 屏幕空间插值生成新顶点，此时已近经过透视除法，z信息已经没有作用
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <param name="t"></param>
/// <returns></returns>
public static void ScreenSpaceLerpVertex(ref CVertex v, CVertex v1, CVertex v2, float t)
{
v.onePerZ = MathUntil.Lerp(v1.onePerZ, v2.onePerZ, t);
//
v.u = MathUntil.Lerp(v1.u, v2.u, t);
v.v = MathUntil.Lerp(v1.v, v2.v, t);
//
v.color.r = MathUntil.Lerp(v1.color.r, v2.color.r, t);
v.color.g = MathUntil.Lerp(v1.color.g, v2.color.g, t);
v.color.b = MathUntil.Lerp(v1.color.b, v2.color.b, t);
}
/// <summary>
/// 屏幕空间插值生成新顶点，此时已近经过透视除法，z信息已经没有作用
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <param name="t"></param>
/// <returns></returns>
public static CVertex ScreenSpaceLerpVertex(CVertex v1, CVertex v2, float t)
{
CVertex v = new CVertex();
float u = MathUntil.Lerp(left.u, right.u, lerpFactor) * w * (_texture.Width - 1);
float v = MathUntil.Lerp(left.v, right.v, lerpFactor) * w * (_texture.Height - 1);
float r = MathUntil.Lerp(left.color.r, right.color.r, lerpFactor) * w * 255;
float g = MathUntil.Lerp(left.color.g, right.color.g, lerpFactor) * w * 255;
float b = MathUntil.Lerp(left.color.b, right.color.b, lerpFactor) * w * 255;
}
/// <summary>
/// 屏幕空间插值生成新顶点，此时已近经过透视除法，z信息已经没有作用
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <param name="t"></param>
/// <returns></returns>
public static void ScreenSpaceLerpVertex(ref CVertex v, CVertex v1, CVertex v2, float t)
{
v.onePerZ = MathUntil.Lerp(v1.onePerZ, v2.onePerZ, t);
//
v.u = MathUntil.Lerp(v1.u, v2.u, t);
v.v = MathUntil.Lerp(v1.v, v2.v, t);
//
v.color.r = MathUntil.Lerp(v1.color.r, v2.color.r, t);
v.color.g = MathUntil.Lerp(v1.color.g, v2.color.g, t);
v.color.b = MathUntil.Lerp(v1.color.b, v2.color.b, t);
}
/// <summary>
/// 光栅化三角形
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
private void TriangleRasterization(CVertex p1, CVertex p2, CVertex p3)
{
if(p1.point.y == p2.point.y)
{
if(p1.point.y < p3.point.y)
{//平顶
DrawTriangleTop(p1, p2, p3);
}
else
{//平底
DrawTriangleBottom(p3, p1, p2);
}
}
else if (p1.point.y == p3.point.y)
{
if (p1.point.y < p2.point.y)
{//平顶
DrawTriangleTop(p1, p3, p2);
}
else
{//平底
DrawTriangleBottom(p2, p1, p1);
}
}
else if (p2.point.y == p3.point.y)
{
if (p2.point.y < p1.point.y)
{//平顶
DrawTriangleTop(p2, p3, p1);
}
else
{//平底
DrawTriangleBottom(p1, p2, p3);
}
}
else
{//分割三角形
CVertex top = null;
CVertex bottom = null;
CVertex middle = null;
if(p1.point.y > p2.point.y && p2.point.y > p3.point.y)
{
top = p3;
middle = p2;
bottom = p1;
}
else if (p3.point.y > p2.point.y && p2.point.y > p1.point.y)
{
top = p1;
middle = p2;
bottom = p3;
}
else if (p2.point.y > p1.point.y && p1.point.y > p3.point.y)
{
top = p3;
middle = p1;
bottom = p2;
}
else if (p3.point.y > p1.point.y && p1.point.y > p2.point.y)
{
top = p2;
middle = p1;
bottom = p3;
}
else if(p1.point.y > p3.point.y && p3.point.y > p2.point.y)
{
top = p2;
middle = p3;
bottom = p1;
}
else if (p2.point.y > p3.point.y && p3.point.y > p1.point.y)
{
top = p1;
middle = p3;
bottom = p2;
}
//插值求中间点x
float middlex = (middle.point.y - top.point.y) * (bottom.point.x - top.point.x) / (bottom.point.y - top.point.y) + top.point.x;
float dy = middle.point.y - top.point.y;
float t = dy / (bottom.point.y - top.point.y);
//插值生成左右顶点
CVertex newMiddle = new CVertex();
newMiddle.point.x = middlex;
newMiddle.point.y = middle.point.y;
MathUntil.ScreenSpaceLerpVertex(ref newMiddle, top, bottom, t);
//平底
DrawTriangleBottom(top, newMiddle, middle);
//平顶
DrawTriangleTop(newMiddle, middle, bottom);
}
}
/// <summary>
/// 从齐次剪裁坐标系转到屏幕坐标
/// </summary>
private void TransformToScreen(CVertex v)
{
if(v.point.w != 0)
{
//先进行透视除法，转到cvv
v.point.x *= 1 / v.point.w;
v.point.y *= 1 / v.point.w;
v.point.z *= 1 / v.point.w;
v.point.w = 1;
//cvv到屏幕坐标
v.point.x = (v.point.x + 1) * 0.5f * this.MaximumSize.Width;
v.point.y = (1 - v.point.y) * 0.5f * this.MaximumSize.Height;
}
}
/// <summary>
/// 进行mvp矩阵变换，将顶点变换到齐次裁剪空间
/// </summary>
private void SetMVPTransform(CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p, CVertex vertex)
{
vertex.point = vertex.point * m;
VectorMatrixTestCase.showVector3(vertex.point);
vertex.point = vertex.point * v;
VectorMatrixTestCase.showVector3(vertex.point);
vertex.point = vertex.point * p;
VectorMatrixTestCase.showVector3(vertex.point);
//得到齐次裁剪空间的点 v.point.w 中保存着原来的z(具体是z还是-z要看使用的投影矩阵,我们使用投影矩阵是让w中保存着z)
//onePerZ 保存1/z，方便之后对1/z关于x’、y’插值得到1/z’
vertex.onePerZ = 1 / vertex.point.w;
//校正的推论： s/z、t/z和x’、y’也是线性关系。而我们之前知道1/z和x’、y’是线性关系。则我们得出新的思路：对1/z关于x’、y’插值得到1/z’，然后对s/z、t/z关于x’、y’进行插值得到s’/z’、t’/z’，然后用s’/z’和t’/z’分别除以1/z’，就得到了插值s’和t’
//这里将需要插值的信息都乘以1/z 得到 s/z和t/z等，方便光栅化阶段进行插值
vertex.u *= vertex.onePerZ;
vertex.v *= vertex.onePerZ;
//
vertex.color.r *= vertex.onePerZ;
vertex.color.g *= vertex.onePerZ;
vertex.color.b *= vertex.onePerZ;
}
/// <summary>
/// 扫描线填充
/// </summary>
/// <param name="left">左端点，值已经经过插值</param>
/// <param name="right">右端点，值已经经过插值</param>
private void ScanlineFill(CVertex left, CVertex right, int yIndex)
{
float dx = right.point.x - left.point.x;
for (float x = left.point.x; x <= right.point.x; x++)
{
int xIndex = (int)(System.Math.Round(x, MidpointRounding.AwayFromZero));
if (xIndex >= 0 && xIndex < this.MaximumSize.Width)
{
float lerpFactor = 0;
if(dx != 0)
{
lerpFactor = (x - left.point.x) / dx;
}
//1/z’与x’和y'是线性关系的
float onePreZ = MathUntil.Lerp(left.onePerZ, right.onePerZ, lerpFactor);
if (onePreZ >= _zBuff[yIndex, xIndex])//使用1/z进行深度测试
{//通过测试
float w = 1 / onePreZ;
_zBuff[yIndex, xIndex] = onePreZ;
//uv 插值，求纹理颜色
float u = MathUntil.Lerp(left.u, right.u, lerpFactor) * w * (_texture.Width - 1);
float v = MathUntil.Lerp(left.v, right.v, lerpFactor) * w * (_texture.Height - 1);
int uIndex = (int)(u + 0.5f);
int vIndex = (int)(v + 0.5f);
uIndex = MathUntil.Range(uIndex, 0, _texture.Width - 1);
vIndex = MathUntil.Range(vIndex, 0, _texture.Height - 1);
//uv坐标系采用dx风格
System.Drawing.Color textrueColor = _texture.GetPixel(vIndex, uIndex);
//插值顶点颜色
float r = MathUntil.Lerp(left.color.r, right.color.r, lerpFactor) * w * 255;
float g = MathUntil.Lerp(left.color.g, right.color.g, lerpFactor) * w * 255;
float b = MathUntil.Lerp(left.color.b, right.color.b, lerpFactor) * w * 255;
//更新渲染模式渲染
if (RenderMode.Textured == _currentMode)
{
_frameBuff.SetPixel(xIndex, yIndex, textrueColor);
}
else if (RenderMode.VertexColor == _currentMode)
{
_frameBuff.SetPixel(xIndex, yIndex, System.Drawing.Color.FromArgb((int)r, (int)g, (int)b));
}
}
}
}
}
//x = (y-y1) * (x2-x1) / (y2-y1) + x1
/// <summary>
/// 平顶，p1,p2,p3为下顶点
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
private void DrawTriangleTop(CVertex p1, CVertex p2, CVertex p3)
{
for (float y = p1.point.y; y <= p3.point.y; y++)
{
int yIndex = (int)(System.Math.Round(y, MidpointRounding.AwayFromZero));
if (yIndex >= 0 && yIndex < this.MaximumSize.Height)
{
float xl = (y - p1.point.y) * (p3.point.x - p1.point.x) / (p3.point.y - p1.point.y) + p1.point.x;
float xr = (y - p2.point.y) * (p3.point.x - p2.point.x) / (p3.point.y - p2.point.y) + p2.point.x;
float dy = y - p1.point.y;
float t = dy / (p3.point.y - p1.point.y);
//插值生成左右顶点
CVertex new1 = new CVertex();
new1.point.x = xl;
new1.point.y = y;
MathUntil.ScreenSpaceLerpVertex(ref new1, p1, p3, t);
//
CVertex new2 = new CVertex();
new2.point.x = xr;
new2.point.y = y;
MathUntil.ScreenSpaceLerpVertex(ref new2, p2, p3, t);
//扫描线填充
if (new1.point.x < new2.point.x)
{
ScanlineFill(new1, new2, yIndex);
}
else
{
ScanlineFill(new2, new1, yIndex);
}
}
}
}
/// <summary>
/// 绘制三角形
/// </summary>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="p3"></param>
/// <param name="mvp"></param>
private void DrawTriangle(CVertex p1, CVertex p2, CVertex p3, CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p)
{
//--------------------几何阶段---------------------------
//变换到齐次裁剪空
SetMVPTransform(m, v, p, p1);
SetMVPTransform(m, v, p, p2);
SetMVPTransform(m, v, p, p3);
////裁剪
if (Clip(p1) == false || Clip(p2) == false || Clip(p3) == false)
{
return;
}
//背面消隐
//if (BackFaceCulling(p1, p2, p3) == false)
//{
// return;
//}
//变换到屏幕坐标
TransformToScreen(p1);
VectorMatrixTestCase.showVector3(p1.point);
TransformToScreen(p2);
VectorMatrixTestCase.showVector3(p2.point);
TransformToScreen(p3);
VectorMatrixTestCase.showVector3(p3.point);
//--------------------光栅化阶段---------------------------
//todo test
//_frameBuff.SetPixel((int)p1.point.x, (int)p1.point.y, System.Drawing.Color.White);
//_frameBuff.SetPixel((int)p2.point.x, (int)p2.point.y, System.Drawing.Color.White);
//_frameBuff.SetPixel((int)p3.point.x, (int)p3.point.y, System.Drawing.Color.White);
TriangleRasterization(p1, p2, p3);
}
/// <summary>
/// 绘制平面
/// </summary>
/// <param name="vIndex1">顶点索引</param>
/// <param name="vIndex2">顶点索引</param>
/// <param name="vIndex3">顶点索引</param>
/// <param name="vIndex4">顶点索引</param>
/// <param name="mvp">mvp矩阵</param>
private void DrawPanel(int vIndex1, int vIndex2, int vIndex3, int vIndex4, CMatrix4x4 m, CMatrix4x4 v, CMatrix4x4 p)
{
CVertex p1 = new CVertex(mesh[vIndex1]);
CVertex p2 = new CVertex(mesh[vIndex2]);
CVertex p3 = new CVertex(mesh[vIndex3]);
//
DrawTriangle(p1, p2, p3, m, v, p);
p1 = new CVertex(mesh[vIndex1]);
p3 = new CVertex(mesh[vIndex3]);
CVertex p4 = new CVertex(mesh[vIndex4]);
DrawTriangle(p3, p4, p1, m, v, p);
}
/// <summary>
/// 检查是否裁剪这个顶点,简单的cvv裁剪,在透视除法之前
/// </summary>
/// <returns>是否通关剪裁</returns>
private bool Clip(CVertex v)
{
//cvv为 x-1,1 y-1,1 z0,1
if(v.point.x >= -v.point.w && v.point.x <= v.point.w &&
v.point.y >= -v.point.w && v.point.y <= v.point.w &&
v.point.z >= 0f && v.point.z <= v.point.w)
{
return true;
}
return false;
}
/// <summary>
/// 背面消隐
/// </summary>
/// <returns>是否通关背面消隐测试</returns>
private bool BackFaceCulling(CVertex p1, CVertex p2, CVertex p3)
{
CVector3D v1 = p2.point - p1.point;
CVector3D v2 = p3.point - p2.point;
CVector3D normal = CVector3D.Cross(v1, v2);
CVector3D viewDir = new CVector3D(0,0,1);//由于在剪裁空间，视线一点是这个方向
if (CVector3D.Dot(normal,viewDir) > 0)
{
return true;
}
return false;
}