/// <summary>
/// Copy constructor.
/// </summary>
/// <param name="?"></param>
public Vector(Vector vectSource)
{
if (vectSource == null)
throw new Exception("Error in Vector.Vector() - source vector cannot be null.");
Resize(vectSource.arrVector.Length, false);
for (int iIndex = 0; iIndex < vectSource.arrVector.Length; iIndex++)
{
arrVector[iIndex] = vectSource.arrVector[iIndex];
}
}
private Color VectorToColor(Vector vectColor)
{
vectColor = vectColor.Limit(0, 1.0);
Color clNewColor = Color.FromArgb((int)(vectColor[0] * 255), (int)(vectColor[1] * 255.0),
(int)(vectColor[2] * 255.0));
return clNewColor;
}
private Vector ColorToVector(Color clColor){
Vector vectColor = new Vector(3, true);
vectColor[0] = clColor.R / 255.0; // red component
vectColor[1] = clColor.G / 255.0; // green component
vectColor[2] = clColor.B / 255.0; // blue component
return vectColor;
}
public void SetupVectA()
{
vectA = new Vector(3);
vectA[0] = 2;
vectA[1] = -1;
vectA[2] = 1;
}
public PointLightSource(double dXPos, double dYPos, double dZPos)
{
vectPosition = new Vector(dXPos, dYPos, dZPos);
}
public override double IntersectionTest(Vector vectRay, Vector vectOrigin)
{
throw new Exception("The method or operation is not implemented.");
}
public override double IntersectionTest(Vector vectRayStart, Vector vectRayEnd)
{
Vector vectRayDirection = (vectRayEnd - vectRayStart).Normalize();
double dA = vectRayDirection.DotProduct(vectRayDirection);
Vector vectSphereToRayOrigin = vectRayStart - vectPosition;
double dB = 2 * vectRayDirection.DotProduct(vectSphereToRayOrigin);
double dC = (vectSphereToRayOrigin).DotProduct(vectSphereToRayOrigin) - (dRadius * dRadius);
double dDiscriminant = (dB * dB) - (4 * dA * dC);
double dt = 0;
double dt1, dt2;
if (dDiscriminant >= 0) // has a solution
{
dt1 = (-dB - Math.Sqrt(dDiscriminant)) / (2.0 * dA);
dt2 = (-dB + Math.Sqrt(dDiscriminant)) / (2.0 * dA);
if (dt1 < dt2)
dt = dt1;
else
dt = dt2;
}
return dt;
}
/// <summary> /// An interstion test performs an analysis along a ray to determine if /// the ray passes through a 3d object in a scene. The value returned /// reflect the point along that ray where the insesction begins. /// /// If zero is returned, then no intersection has occured. /// /// To get the actual 3D position where the intersection occured, use the /// following formula (where t is a possible value returned): /// /// p(t) = o + t(s - o) /// /// Where o is the origin position (vectOrigin), t is the value returned /// by this method, and s is the direction vector (vectRay). /// </summary> public abstract double IntersectionTest(Vector vectRayStart, Vector vectRayEnd);
/// <summary>
/// Creates a new vector that is the unit vector for
/// for this vector.
/// </summary>
public Vector Normalize()
{
if (arrVector == null)
return new Vector(0);
Vector vectNormalized = new Vector(arrVector.Length, true);
double dUnitLength = Length;
if (arrVector != null && dUnitLength > 0)
{
for (int iIndex = 0; iIndex < arrVector.Length; iIndex++)
{
vectNormalized[iIndex] = arrVector[iIndex] / dUnitLength;
}
}
return vectNormalized;
}
/// <summary>
/// Returns the dot product of this and the second provided vector,
/// </summary>
/// <param name="vect"></param>
/// <returns></returns>
public double DotProduct(Vector vect)
{
if (vect == null)
return 0;
if (vect.arrVector == null || arrVector == null)
throw new Exception ("Error in Vector.DotProduct(). The vector cannot be a null vector.");
if (vect.Size != Size)
throw new Exception ("Error in Vector.DotProduct(). Both vectors cannot be of the same size.");
double dResult = 0;
for (int iIndex = 0; iIndex < arrVector.Length; iIndex++)
{
dResult += vect.arrVector[iIndex] * arrVector[iIndex];
}
return dResult;
}
/// <summary>
/// Calculates the angle betweeen two vectors. Angle returned is in degrees.
/// </summary>
public double Angle(Vector vect)
{
double dVal = DotProduct(vect) / (Length * vect.Length);
return Math.Acos(dVal) * (180.0 / Math.PI);
}
public static Vector operator* (Vector vect1, Vector vect2) {
if (vect1 == null || vect2 == null)
throw new NullReferenceException();
if (vect1.arrVector == null || vect2.arrVector == null)
throw new Exception("Multiplying by null vector is not permitted.");
if (vect1.arrVector.Length != vect2.arrVector.Length)
throw new Exception("Multiplying two vectors together by different lengths is not permitted.");
Vector vectResult = new Vector(vect1.arrVector.Length, true);
for (int iIndex = 0; iIndex < vect1.arrVector.Length; iIndex++)
{
vectResult.arrVector[iIndex] = vect1.arrVector[iIndex] * vect2.arrVector[iIndex];
}
return vectResult;
}
public static Vector operator* (Vector vect, double dVal)
{
if (vect == null)
throw new NullReferenceException();
if (vect.arrVector == null)
throw new Exception("Scaling a null vector is not permitted.");
Vector vectResult = new Vector(vect.arrVector.Length, true);
for (int iIndex = 0; iIndex < vect.arrVector.Length; iIndex++)
{
vectResult.arrVector[iIndex] = dVal * vect.arrVector[iIndex];
}
return vectResult;
}
public static Vector operator- (Vector vect1, Vector vect2)
{
if (vect1 == null || vect2 == null)
throw new NullReferenceException();
if (vect1.arrVector == null || vect2.arrVector == null)
throw new Exception("Subtraction of null vectors is not permitted.");
if (vect1.arrVector.Length != vect2.arrVector.Length)
throw new Exception("Cannot subtract - vectors are not of the same size.");
Vector vectResult = new Vector(vect1.arrVector.Length, true);
for (int iIndex = 0; iIndex < vect1.arrVector.Length; iIndex++)
{
vectResult.arrVector[iIndex] = vect1.arrVector[iIndex] - vect2.arrVector[iIndex];
}
return vectResult;
}
public void SetupVectB()
{
vectB = new Vector(3);
vectB[0] = 1;
vectB[1] = 1;
vectB[2] = 2;
}
public Camera(double dXPos, double dYPos, double dZPos,
double dLookAtX, double dLookAtY, double dLookAtZ,
double dUpX, double dUpY, double dUpZ)
{
vectPosition = new Vector(dXPos, dYPos, dZPos);
vectLookAt = new Vector(dLookAtX, dLookAtY, dLookAtZ);
vectUp = new Vector(dUpX, dUpY, dUpZ);
}
public Object3D(double dXPos, double dYPos, double dZPos)
{
vectPosition = new Vector(dXPos, dYPos, dZPos);
}
/// <summary>
/// Adjusts the values of a vector so that they are within
/// the limits imposed by Min and Max.
/// </summary>
/// <param name="dMin"></param>
/// <param name="dMax"></param>
/// <returns></returns>
public Vector Limit(double dMin, double dMax)
{
if (arrVector == null)
return new Vector(0);
if (dMin > dMax)
{
double dTemp = dMin;
dMin = dMax;
dMax = dTemp;
}
Vector vectLimited = new Vector(arrVector.Length, true);
for (int iIndex = 0; iIndex < vectLimited.Size; iIndex++)
{
if (arrVector[iIndex] < dMin)
vectLimited[iIndex] = dMin;
else if (arrVector[iIndex] > dMax)
vectLimited[iIndex] = dMax;
else
vectLimited[iIndex] = arrVector[iIndex];
}
return vectLimited;
}
public abstract Vector GetSurfaceNormal(Vector vectSurfacePosition);
/// <summary>
/// Copy constructor with a vector.
/// </summary>
public Matrix (Vector vect)
{
Assign(vect);
}
public override Vector GetSurfaceNormal(Vector vectSurfacePosition)
{
return (vectSurfacePosition - vectPosition).Normalize();
}
/// <summary>
/// Makes the matrix an exact duplicate of the provided vector.
/// </summary>
public void Assign(Vector vect)
{
int iColumns = vect.Size;
arrMatrix = Create2DArray(1, iColumns);
if (arrMatrix == null)
return;
for (int iCol = 0; iCol < iColumns; iCol++)
{
arrMatrix[0, iCol] = vect[iCol];
}
}
public override Vector GetSurfaceNormal(Vector vectSurfacePosition)
{
Vector vectNormal = (vectSurfacePosition - vectPosition).Normalize(); // *(1.0 / dSize);
return vectNormal;
}
/// <summary>
/// Multiplies a vector by the matrix in order to produce a new vector.
/// An exception is thrown if the vector has a size that is not equal
/// to then number of rows in the matrix, or if the matrix is null or
/// vector is null. Equivalent to VECT * MAT = VECT
/// </summary>
public Vector Multiply(Vector vect)
{
if (vect == null)
throw new NullReferenceException("Error in Matrix.Multiply." +
"Provided vector object is null.");
if (arrMatrix == null)
throw new Exception("Error in Matrix.Multiply. " +
"This matrix is a null matrix.");
if (vect.IsNull)
throw new Exception("Error in Matrix.Multiply. " +
"Provided vector is a null vector.");
int iRows = Rows;
int iColumns = Columns;
if (iRows != vect.Size)
throw new Exception("Error in Matrix.Multiply. " +
"The number vector is not the same size as the number " +
"of rows in the matrix.");
// convert the vector to a matrix
Matrix matResult = new Matrix(vect);
matResult = matResult.Multiply(this);
// create a new matrix that is of the same # or rows as the result
Vector vectResult = new Vector(iColumns);
for (int iIndex = 0; iIndex < iColumns; iIndex++)
{
vectResult[iIndex] = matResult[0, iIndex];
}
return vectResult;
}
private Vector TraceRay(Vector vectRayStart, Vector vectRayEnd, int iRayCount)
{
// establish a vector of base intenisites (current "black").
Vector vectIntensity = new Vector(3);
Vector vectSpecular = new Vector(3);
// make sure we don't recurse any more than we have to
if (iRayCount > iMaxRecursion)
return vectIntensity;
// first, find the object that intersects the ray at the start position
Object3D obj3dClosest = null;
double dtClosest = 0;
for (int iIndex = 0; iIndex < arrObjects.Count; iIndex++)
{
Object3D obj3dCurrent = (Object3D)arrObjects[iIndex];
if (obj3dCurrent == null)
continue;
// convert the object to eye coordinates
double dtCurrent = obj3dCurrent.IntersectionTest(vectRayStart, vectRayEnd);
// check for any intersection
if (dtCurrent <= 0)
continue;
// intersection - ray has hit an object
if (obj3dClosest == null || dtCurrent < dtClosest)
{
obj3dClosest = obj3dCurrent;
dtClosest = dtCurrent;
}
}
// no object intersect the ray, so return black, or 0 intensity
if (obj3dClosest == null)
return vectIntensity;
// shadow ray flag
bool bIsShadowRay = false;
// establish a base intensity of the object
vectIntensity = vectAmbientLightIntensity * vectAmbientLightColor * obj3dClosest.AmbientColor;
// now, go through all point light sources, and see if it
// influences the color of the light
// get 3d position where the ray touched the object
Vector vectRay = (vectRayEnd - vectRayStart).Normalize();
Vector vectSurfacePoint = vectRayStart + dtClosest * vectRay;
// get the normal of the surface hit
Vector vectSurfaceNormal = obj3dClosest.GetSurfaceNormal(vectSurfacePoint);
// tiny adjustment
vectSurfacePoint += (vectSurfaceNormal * 0.01);
for (int iIndex = 0; iIndex < arrPointLightSources.Count; iIndex++)
{
// get the point light source in the scene
PointLightSource plsLight = (PointLightSource)arrPointLightSources[iIndex];
if (plsLight == null)
continue;
bIsShadowRay = false;
// convert the light source to UVW coodinates
//Vector vectLightRay = plsLight.Position - vectSurfacePoint;
// test to see how far away the light intersects the vector
// dt = obj3dClosest.IntersectionTest(plsLight.Position, vectSurfacePoint);
// test to see if the ray is in the shadow of another object wrt
// the light source - assuming that the light ray to the surface of
// of the object is 1.0, then any objects between the light source
// and the current object will have a value between 0 and 1
for (int iIndex2 = 0; iIndex2 < arrObjects.Count; iIndex2++)
{
Object3D obj3dCurrent = (Object3D)arrObjects[iIndex2];
if (obj3dCurrent == null || obj3dClosest == obj3dCurrent)
continue;
dtClosest = obj3dCurrent.IntersectionTest(vectSurfacePoint, plsLight.Position);
// yes, there is another object in the way of this object, so the
// ray cast by the light source is actually a shadow ray for this object
if (dtClosest > 0)
{
bIsShadowRay = true;
break;
}
}
// if the ray is a shadow ray, then the light from the light source does not contribute
// to the light in the ray, so just continue on to the next light source
if (bIsShadowRay)
continue;
// ok, so the light source contributes to the light shown on the object
Vector vectLightVector = (plsLight.Position - vectSurfacePoint).Normalize();
//Vector vectLightVector = new Vector(0, 1, 0);
// calculate diffuse component of the light source
Vector vectDiffuse = (plsLight.Diffuse * obj3dClosest.DiffuseColor *
vectSurfaceNormal.DotProduct(vectLightVector)).Limit(0,1);
vectIntensity += vectDiffuse;
// get the inverse of the viewing ray
// calculate specular component of the light source
// get the "Halfway" vector
Vector vectH = (vectLightVector + vectRay * -1).Normalize();
vectSpecular = (plsLight.Specular * obj3dClosest.SpecularColor *
Math.Pow(vectH.DotProduct(vectSurfaceNormal), obj3dClosest.SpecularPow)).Limit(0, 1);
vectIntensity += vectSpecular;
}
Vector vectRecursiveRay = vectRay - (2 * vectRay.DotProduct(vectSurfaceNormal) * vectSurfaceNormal);
Vector vectReflectiveIntensity = (TraceRay(vectSurfacePoint, vectRecursiveRay + vectSurfacePoint,
++iRayCount)).Limit(0, 1);
vectIntensity += obj3dClosest.SpecularColor * vectReflectiveIntensity;
// add the final and reflective colors together
return vectIntensity; // +vectReflectiveIntensity;
}
public static Vector CrossProduct(Vector vectA, Vector vectB)
{
if (vectA == null || vectB == null)
throw new NullReferenceException();
if (vectA.Size == 0 || vectB.Size == 0)
throw new Exception("Error in MatrixMath.CrossProduct. Neither vector can be a null vector.");
if (vectA.Size != 3 || vectB.Size != 3)
throw new Exception("Error in MatrixMath.CrossProduct. Both vectors must be of size 3.");
return new Vector(
vectA[1] * vectB[2] - vectA[2] * vectB[1],
vectA[2] * vectB[0] - vectA[0] * vectB[2],
vectA[0] * vectB[1] - vectA[1] * vectB[0]);
}
