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This chapter demonstrates the transformation of geometric shapes in 3D space, focusing on a triangle, circle, and cone. We rotate a triangle around the line y = -2 using translation and rotation matrices, yielding varied orientations. The section also presents the construction of circles and rings, detailing their equations and vertices. Finally, we illustrate cone drawing utilizing triangle fans for lateral and base surfaces. The programming logic applies to real-time transformations for dynamic visual effects in graphics applications.
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Ring, Circle, Cone Chapter 4
Triangle rotating We have a trianglein the following position Y (-2,1.73) X (-1,0) (-3,0) 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).
Set vertex private 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(); }
Set Rotation private 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
Make a Ring We have a ringin the following position with inner radius 0.5 and the outer radius 1. Y (1,0) (3,0) X (2,0) Both circles has equation
Set Ring vertex private void SetRingVertex() { v_ring = new CustomVertex.PositionColored[122]; float theta = 2.0f*(float)Math.PI/60.0f; // 6º for(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 circle v_ring[2*k].Color=Color.Red.ToArgb(); // red v_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 circle v_ring[2*k+1].Color=Color.White.ToArgb(); //white }
Multiple Rotations private 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; }
Draw Ring VBR = 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(); // omit adding event handling code m_device.SetStreamSource( 0, VBR, 0); SetRotationR(); m_device.DrawPrimitives(PrimitiveType.TriangleStrip, 0, 120);
Make a Circle If we have a circle center at (2,0)with radius 1. Y (1,0) (3,0) X (2,0) The circles has equation
Set Circle vertex private 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 center v_ circle[0].Color=Color.Red.ToArgb(); // red float theta = 2.0f*(float)Math.PI/60.0f; // 6º for(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; // circle v_ circle[k].Color=Color.White.ToArgb(); //white }
Draw Circle code m_device.SetStreamSource( 0, VBCircle, 0); SetRotationR(); m_device.DrawPrimitives(PrimitiveType.TriangleFan, 0, 60);
Direction of a triangle Any triangle has 3 vertices v1, v2, v2. Suppose we draw this triangle with order v1 v2v2. v2 v3 v2 v1 v3 v1 clockwise counter-clockwise Then this direction could be either clockwise or anti-clockwise ( counter-clockwise)
SetCULLMODE If we do not want to draw clockwise triangle only then set If we do not want to draw anti-clockwise triangle only then set m_device.RenderState.CullMode = Cull.Clockwise; Note: When drawing Triangle Strip, the first one must be clockwise, the followings could be any directions. m_device.RenderState.CullMode = Cull.CounterClockwise; If we want to draw all direction triangle then set m_device.RenderState.CullMode = Cull.None;
Draw Cone Cube 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.
Set Cone Vertex • void 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(); • } • }
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(); • }
