一、三維空間多段線幾何
1 應用背景
opengl常用glLineWidth命令設定線寬，此線寬在透視投影中不會隨著相機遠近變化而縮放。專案中高版本glLineWidth命令失效，需要考慮如何快速、方便、寬度不變的多段線幾何。方案a：純shader繪製曲線，繪製到一個二維平面上，然後將平面旋轉朝向螢幕，保持平面縮放不變，實現中需要考慮繪製順序，因為失去了深度，沒辦法做深度測試。方案b：傳前一個點和後一個點到頂點屬性中去，使用幾何著色器，將線寬對應的新頂點傳送出去，實現起來還是比較二維，從另外的視角觀察直線會被摺疊。方案c：手動生成每一線段幾何面片，組合所有面片為一個drawable，實現中遇到有線段連線處不光滑、固定線寬等問題，總體上基本和glLineWidth繪製的線效果一致。ps：根據國外部落格學到了方案4，例項化繪製線段技術，實現起來效果很不錯，優法！
2 單個線段幾何生成
如上圖所示，三維線段幾何可以抽象為圓柱體，圓柱體的半徑為線寬，高度為上下底面M和N構成的向量MN長度之差。注意到圓柱體進一步離散化為多面體，我們只需要側邊包圍面，將其展開就得到了長方形。長方形的長為底面周長，高為MN長度。注意到，多段線的線段間即有平移也有旋轉，幾何座標要乘以旋轉矩陣。
void constructSegment(osg::Vec3 firstPt,osg::Vec3 secondPt,float width)
{
osg::ref_ptr<osg::Vec3Array> vertices=new osg::Vec3Array;
osg::ref_ptr<osg::DrawElementsUInt> sides=new osg::DrawElementsUInt(osg::PrimitiveSet::TRIANGLE_FAN);
int numSegments=10;
float radius=0.5*width;
auto center=(firstPt+secondPt)*0.5;
float height=(firstPt-secondPt).length();
float basez=-height*0.5f;
float topz=height*0.5f;
auto dir=firstPt-secondPt；
osg::Quat rotQuat;
rotQuat.makeRotate(osg::Z_AXIS,dir);
float angle=0.0f;
float angleDelta=2.f*M_PI/(float)numSegments;
for(int bodyi=0;bodyi<numSegments;++bodyi,angle+=angleDelta)
{
float c=cosf(angle);
float s=sinf(angle);
auto P=osg::Vec3(c*radius,s*radius,topz);
auto Q=osg::Vec3(c*radius,s*radius,topz);
P=P*osg::Matrix:;rotate(rotQuat)*osg::Matrix::translate(center);
Q=Q*osg::Matrix:;rotate(rotQuat)*osg::Matrix::translate(center);
vertices->push_back(P);
vertices->push_back(Q);
}
//新增圓柱索引
float curSegmentSize=0;
for(int i=0;i<numSegments*2-2;i+=2)
{
sides->push_back(curSegmentSize+i);
sides->push_back(curSegmentSize+i+1);
sides->push_back(curSegmentSize+i+3);
sides->push_back(curSegmentSize+i+2);
sides->push_back(curSegmentSize+i);
sides->push_back(curSegmentSize+i+3);
}
sides->push_back(curSegmentSize+numSegments*2-2);
sides->push_back(curSegmentSize+numSegments*2-1);
sides->push_back(curSegmentSize+1);
sides->push_back(curSegmentSize);
sides->push_back(curSegmentSize+numSegments*2-2);
sides->push_back(curSegmentSize+1);
}
最佳化：按照圓柱的方式，生成的多段線幾何之間的連線不光滑，且會隨著相機縮放而縮放，因此通常在兩段線之間新增半圓球過渡。
void constructHalfSphere(osg::ref_ptr<osg::Vec3Array> vertices,osg::ref_ptr<osg::DrawElementsUInt> sides,osg::Vec3 firstPt,osg::Vec3 secondPt,float radius,int&curSegmentSize,bool isTop)
{
int numRows=5;
int numSegments=5;
float lDelta=M_PI/(float)numRows;
float vDelta=1.f/(float)numRows;
float angleDelta=M_PI*2.f/(float)numSegments;
float lBase=-M_PI*0.5f+(isTop?(lDelta*(numRows/2)):0.f);
float rBase=isTop?(cosf(lBase)*radius):0.f;
float zBase=isTop?(sinf(lBase)*radius):-radius;
float vBase=isTop?(vDelta*(numRows/2)):0.f;
float nzBase=isTop?(sinf(lBase)):-1.f;
float nRatioBase=isTop?(cosf(lBase)):0.f;
int rowbegin=isTop:numRows/2:0;
int rowend=isTop?numRows:numRows/2;
auto dir=(firstPt-secondPt);
osg::Quat rotQuat;
rotQuat.makeRoate(osg::Z_AXIS,dir);
for(int rowi=rowbegin;rowi<rowend;++rowi)
{
float lTop=lBase+lDelta;
float rTop=cosf(lTop)*radius;
float zTop=sinf(lTop)*radius;
float vTop=vBase+vDelta;
float nzTop=sinf(lTop);
float nRatioTop=cosf(lTop);
float angle=0.0f;
for(int topi=0;topi<numSegments;++topi,angle+=angleDelta)
{
float c=cosf(angle);
float s=sinf(angle);
auto P=osg::Vec3(c*rTop,s*rTop,zTop);
auto Q=osg::Vec3(c*rBase,s*rBase,zBase);
P=P*osg::Matrixd::Rotate(rotQuat)*osg::Matrix::translate(isTop?firstPt:secondPt);
Q=Q*osg::Matrixd::Rotate(rotQuat)*osg::Matrix::translate(isTop?firstPt:secondPt);
vertices->push_back(P);
vertices->push_back(Q);
}
//新增圓柱索引
for(int i=0;i<numSegments*2-2;i+=2)
{
sides->push_back(curSegmentSize+i);
sides->push_back(curSegmentSize+i+1);
sides->push_back(curSegmentSize+i+3);
sides->push_back(curSegmentSize+i+2);
sides->push_back(curSegmentSize+i);
sides->push_back(curSegmentSize+i+3);
}
sides->push_back(curSegmentSize+numSegments*2-2);
sides->push_back(curSegmentSize+numSegments*2-1);
sides->push_back(curSegmentSize+1);
sides->push_back(curSegmentSize);
sides->push_back(curSegmentSize+numSegments*2-2);
sides->push_back(curSegmentSize+1);
curSegmentSize+=numSegments*2;
lBase=lTop;
rBase=rTop;
zBase=zTop;
vBase=vTop;
nzBase=nzTop;
nRatioBase=nRatioTop;
}
return true;
}
3 例項化渲染線條技術
3.1 例項化技術簡介
當你要繪製大量重複的幾何時，如果透過繫結vbo、上傳頂點、呼叫繪製命令的方式會導致幀率急劇下降而卡頓。因為與GPU繪製本身相比，切換上下文，從CPU到GPU慢得多。例項化技術就是使用一個繪製函式，讓GPU利用這些資料繪製多個物體，節省了每次繪製物體時CPU到GPU的通訊。opengl中呼叫命令為：glDrawArraysInstanced和glDrawElementsInstanced。
首先考慮繪製單個線段，對於三維線段，可以傳遞線段起點、終點座標，以及線段頂點為圖元屬性，然後在頂點著色器中將矩形圖元頂點座標變換到合適位置。如下圖所示，已知A、B世界座標，先求得AB的方向向量沿x軸，然後再求沿y軸的垂直向量，依次計算兩個三角形圖元的頂點座標。
std::vector<osg::Vec3> linePoints;
{
///建立四邊形頂點
auto vertices=new osg::Vec3Array;
vertices->push_back(osg::Vec3(0,-0.5,0));
vertices->push_back(osg::Vec3(0,-0.5,1));
vertices->push_back(osg::Vec3(0,0.5,1));
vertices->push_back(osg::Vec3(0,-0.5,0));
vertices->push_back(osg::Vec3(0,0.5,1));
vertices->push_back(osg::Vec3(0,0.5,0));
///建立幾何起點和終點
auto pointAs=new osg::Vec3Array;
auto pointBs=new osg::Vec3Array;
pointAs->push_back(linePoints.front());
for(int i=1;i<=linePoints.size()-1;i++)
{
pointAs->push_back(linePoints[i]);
pointBs->push_back(linePoints[i]);
}
pointBs->push_back(linePoints.back());
///建立四邊形幾何
osg::ref_ptr<osg::Geometry> quad=new osg::Geometry;
quad->setVertexAttribArray(0,vertices,osg::Array::BIND_PER_VERTEX);
quad->setVertexAttribArray(1,pointAs,osg::Array::BIND_PER_VERTEX);
quad->setVertexAttribArray(2,pointBs,osg::Array::BIND_PER_VERTEX);
quad->addPrimitiveSet(new osg::DrawArrays(GL_TRIANGLES,0,6,pointAs->size()));
quad->setusedisplayList(false);
quad->setUseVertexBufferObjects(true);
quad->getOrCreateStateSet()->setAttribute(new osg::VertexAttribDivisor(1,1));
quad->getOrCreateStateSet()->setAttribute(new osg::VertexAttribDivisor(2,1));
osg::ref_ptr<osg::Geode> geode=new osg::Geode;
geode->addDrawable(quad);
const char* vertCode=R"(
#version 330 core
layout(location=0) in vec3 aPos;
layout(location=1) in vec3 aPointA;
layout(location=2) in vec3 aPointB;
uniform mat4 osg_ModelViewProjectionMatrix;
uniform mat4 osg_ModelViewMatrix;
uniform mat4 osg_NormalMatrix;
uniform vec2 resolution;
uniform float width=5.0;
void main(){
vec4 clip0=osg_ModelViewProjectionMatrix*vec4(aPointA,1.0);
vec4 clip1=osg_ModelViewProjectionMatrix*vec4(aPointB,1.0);
vec2 screen0=resolution*(0.5*clip0.xy/clip0.w+0.5);
vec2 screen1=resolution*(0.5*clip1.xy/clip1.w+0.5);
vec2 xBasis=normalize(screen1.xy-screen0.xy);
float length=length(screen1.xy-screen0.xy);
vec2 yBasis=vec2(-xBasis.y,xBasis.x);
vec2 pt=screen0+lenthAB*xBasis*aPos.z+width*yBasis*aPos.y;
gl_Position=vec4(clip0.w*(2.0*pt/resolution-1.0),clip0.z,clip0.w);
}
)";
const char* fragCode=R"(
uniform vec3 front;
uniform float opacity;
out vec4 fragColor;
void main()
{
fragColor=vec4(front,opacity);
}
)";
osg::ref_ptr<osg::Shader> vertShader=new osg::Shader(osg::Shader::VERTEX,vertCode);
osg::ref_ptr<osg::Shader> fragShader=new osg::Shader(osg::Shader::FRAGMENT,fragCode);
osg::ref_ptr<osg::Program> program=new osg::Program;
program->addShader(vertShader);
program->addShader(fragShader);
geode->getOrCreateStateSet()->setAttributeAndModes(program,OVERRIDE_ON);
}
二、三維空間圓弧面幾何
1 應用背景
專案中有需求繪製三維的圓弧面幾何。可以按照扇形的方式生成。
2 圓弧面幾何
void constructSector(osg::Vec3 center,osg::Vec3 left,osg::Vec3 right,float radius,osg::Vec3 color,float radius,float width)
{
///建立扇形頂點
osg::ref_ptr<osg::Vec3Array> vertices=new osg::Vec3Array;
///建立扇形法線
osg::ref_ptr<osg::Vec3Array> normals=new osg::Vec3Array;
///建立扇形拓撲
osg::ref_ptr<osg::DrawElementsUInt> sides=new osg::DrawElementsUInt(osg::PrimitiveSet::TRIANGLE_FAN);
int index=0;
///使用球面插值計算圓弧上座標
auto LC=left-center;
auto RC=right-center;
LC.normalize();
RC.normalize();
osg::Quat newQuat,startQuat,endQuat;
startQuat.makeRotate(LC,LC);
endQuat.makeRotate(LC,RC);
vertices->push_back(center);
sides->push_back(index++);
///生成正面
for(float i=0;i<=1;i+=0.02)
{
newQuat.slerp(i,startQuat,endQuat);
auto point=center+LC*osg::Matrix(newQuat)*radius;
vertices->push_back(point);
normals->push_back(osg::Vec3(0,0,1));
sides->push_back(index++);
}
vertices->push_back(center);
sides->push_back(index++);
///生成反面
for(float i=1;i》=0;i-=0.02)
{
newQuat.slerp(i,startQuat,endQuat);
auto point=center+LC*osg::Matrix(newQuat)*radius;
vertices->push_back(point);
normals->push_back(osg::Vec3(0,0,-1));
sides->push_back(index++);
}
///建立扇形幾何
osg::ref_ptr<osg::Geometry> sector=new osg::Geometry;
sector->setVertexArray(vertices);
sector->setNormalArray(normals);
sector->addPrimitiveSet(sides);
}