1

Ring, Circle, Cone

Chapter 4

2

Triangle rotating We have a triangle in the following position

 

     

 

We want to rotate it around line y = 2. For this purpose, we have make a translation T (2,0,0), following a rotation about Y axis, then make the reverse translation T (2,0,0).

(3,0) (1,0)

(2,1.73) Y

X

3

Set vertexprivate void SetVertex(){

verts = new CustomVertex.PositionColored[3];

verts[0].X=-3.0f;verts[0].Y=0.0f;verts[0].Z=0.0f; verts[0].Color = Color.Yellow.ToArgb();

verts[1].X=-1.0f;verts[1].Y=0.0f;verts[1].Z=0.0f; verts[1].Color = Color.FromArgb(0,0,255).ToArgb() ;

verts[2].X=-2.0f; verts[2].Y=1.73f;verts[2].Z=0.0f; verts[2].Color = Color.Red.ToArgb();

}

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Set Rotationprivate void SetRotation(){

float a = (float)Environment.TickCount /1000.0f;float theta = a*2.0f*(float)Math.PI; Matrix mR = Matrix.RotationY(theta) ;Matrix T1 = Matrix.Translation(2.0f, 0.0f, 0.0f); Matrix T2 = Matrix.Translation(-2.0f, 0.0f, 0.0f); Matrix Mat = T1*mR*T2; m_device.Transform.World=Mat;

}

Note: In the combination of matrix, the left matrix takes the Transformation action first. So in the above, T1 first, mR second, T2 last

5

Make a Ring We have a ring in the following position with inner radius 0.5 and the outer radius 1.

 

     

Both circles has equation

(3,0)

Y

X(2,0)

(1,0)

2 cos 2 0.5cosand (0 2π)

sin 0.5sin

x x

y y

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Set Ring vertexprivate void SetRingVertex(){

v_ring = new CustomVertex.PositionColored[122];float theta = 2.0f*(float)Math.PI/60.0f; // 6ºfor(int k=0; k<61; k++){v_ring[2*k].X=2+0.5f*(float)Math.Cos(theta*k);v_ring[2*k].Y=0.5f*(float)Math.Sin(theta*k);

v_ring[2*k].Z=0.0f; // inner circlev_ring[2*k].Color=Color.Red.ToArgb(); // redv_ring[2*k+1].X=2+(float)Math.Cos(theta*k);v_ring[2*k+1].Y=(float)Math.Sin(theta*k);v_ring[2*k+1].Z=0.0f; // outer circlev_ring[2*k+1].Color=Color.White.ToArgb(); //white

}

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Multiple Rotationsprivate void SetRotation(){

float a1 = (float)Environment.TickCount /1000.0f;float theta1 = a1*2.0f*(float)Math.PI; float a2 = (float)Environment.TickCount /1300.0f;float theta2 = a2*2.0f*(float)Math.PI; float a3 = (float)Environment.TickCount /1700.0f;float theta3 = a2*2.0f*(float)Math.PI; Matrix RX = Matrix.RotationY(theta1) ;Matrix RY = Matrix.RotationX(theta2) ;Matrix RZ = Matrix.RotationZ(theta3) ;Matrix T1 = Matrix.Translation(2.0f, 0.0f, 0.0f); Matrix T2 = Matrix.Translation(-2.0f, 0.0f, 0.0f); m_device.Transform.World=T2*RX*RY*RZ*T1;

}

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Draw RingVBR = new

VertexBuffer( typeof(CustomVertex.PositionColored), 122, m_device, 0, CustomVertex.PositionColored.Format, Pool.Default); GraphicsStream stream = VBR.Lock(0, 0, 0);stream.Write(this.v_ring);VBR.Unlock();

m_device.SetStreamSource( 0, VBR, 0);SetRotationR();m_device.DrawPrimitives(PrimitiveType.TriangleStrip, 0,

120);

// omit adding event handling code

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Output

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Make a CircleIf we have a circle center at (2,0) with radius 1.

 

     

The circles has equation

(3,0)

Y

X(2,0)

(1,0)

2 cos(0 2π)

sin

x

y

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Set Circle vertexprivate void SetCircleVertex(){

v_circle[]= new CustomVertex.PositionColored[62];v_circle[0].X=2.0f;v_ circle[0].Y=0.0f;v_ circle[0].Z=0.0f; // circle centerv_ circle[0].Color=Color.Red.ToArgb(); // redfloat theta = 2.0f*(float)Math.PI/60.0f; // 6ºfor(int k=1; k<62; k++){v_circle[k].X=2+(float)Math.Cos(theta*k);

v_ circle[k].Y=(float)Math.Sin(theta*k);v_ circle[k].Z=0.0f; // circlev_ circle[k].Color=Color.White.ToArgb(); //white

}

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Draw Circle codem_device.SetStreamSource( 0, VBCircle, 0);SetRotationR();m_device.DrawPrimitives(PrimitiveType.TriangleFan, 0, 60);

13

Direction of a triangleAny triangle has 3 vertices v1, v2, v2. Suppose we draw this triangle with order v1 v2v2.

v1

v2

v3 v1

v2

v3

Then this direction could be either clockwise or anti-clockwise ( counter-clockwise)

clockwise counter-clockwise

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Set CULLMODE

If we do not want to draw anti-clockwise triangle only then set

m_device.RenderState.CullMode = Cull.Clockwise;

If we do not want to draw clockwise triangle only then set

m_device.RenderState.CullMode = Cull.CounterClockwise;

If we want to draw all direction triangle then set

m_device.RenderState.CullMode = Cull.None;

Note: When drawing Triangle Strip, the first one must be clockwise, the followings could be any directions.

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Draw ConeCube has one lateral surface and one base circle. So we will pick 62 points: one at (0, 2, 0), one is the base circle center (0, 0, 0). Also 61 points at the circle. Radius=1.2

The lateral surface will be draw from method:

PrimitiveType.TriangleFan

the direction is counter-clockwise.

The base circle is also use PrimitiveType.TriangleFan, but the direction is clockwise. Also we need to change the vertex buffer value, during the drawing.

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Set Cone Vertexvoid SetVertex()

{ v_cone = new CustomVertex.PositionColored[62];

v_cone[0].X = 0.0f; v_cone[0].Y = 2.0f; v_cone[0].Z = 0.0f;

v_cone[0].Color =Color.Yellow.ToArgb();

float theta = 2.0f*(float)Math.PI/60.0f;

for(int k=1; k<62; k++) {

v_cone[k].X = 1.2f*(float)Math.Cos(k*theta);

v_cone[k].Y = 0.0f; v_cone[k].Z = 1.2f*(float)Math.Sin(k*theta);

v_cone[k].Color =Color.Blue.ToArgb();

}

}

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void Render() {

. . . . . . . . . . . ..

m_device.Clear(ClearFlags.Target, Color.Black.ToArgb(),1.0f,0);

m_device.BeginScene();

m_device.SetStreamSource( 0, VB, 0);

SetRotation();

m_device.RenderState.CullMode = Cull.Clockwise;

m_device.DrawPrimitives(PrimitiveType.TriangleFan, 0,60);

m_device.RenderState.CullMode = Cull.CounterClockwise;

m_device.DrawPrimitives(PrimitiveType.TriangleFan, 1,59);

m_device.EndScene();

m_device.Present();

}

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Output

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• Need to add Cylinder two colors