/// <summary>sets this to multivector value.
/// </summary>
public void Set(mv src)
{
AllocateGroups(src.gu());
if (m_c[0] != null)
{
c3ga.Copy_1(m_c[0], src.m_c[0]);
}
if (m_c[1] != null)
{
c3ga.Copy_5(m_c[1], src.m_c[1]);
}
if (m_c[2] != null)
{
c3ga.Copy_10(m_c[2], src.m_c[2]);
}
if (m_c[3] != null)
{
c3ga.Copy_10(m_c[3], src.m_c[3]);
}
if (m_c[4] != null)
{
c3ga.Copy_5(m_c[4], src.m_c[4]);
}
if (m_c[5] != null)
{
c3ga.Copy_1(m_c[5], src.m_c[5]);
}
}
public void Set(mv src)
{
if (src.c()[2] != null)
{
float[] ptr = src.c()[2];
m_c[0] = ptr[0];
m_c[1] = ptr[1];
m_c[2] = ptr[2];
m_c[3] = ptr[3];
m_c[4] = ptr[4];
m_c[5] = ptr[5];
m_c[6] = ptr[6];
m_c[7] = ptr[7];
m_c[8] = ptr[8];
m_c[9] = ptr[9];
}
else
{
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
m_c[3] = 0.0f;
m_c[4] = 0.0f;
m_c[5] = 0.0f;
m_c[6] = 0.0f;
m_c[7] = 0.0f;
m_c[8] = 0.0f;
m_c[9] = 0.0f;
}
}
public void Set(mv src)
{
if (src.c()[1] != null)
{
float[] ptr = src.c()[1];
m_c[0] = ptr[1];
m_c[1] = ptr[2];
m_c[2] = ptr[3];
}
else
{
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
}
}
public void Set(mv src)
{
if (src.c()[2] != null)
{
float[] ptr = src.c()[2];
m_c[0] = ptr[7];
m_c[1] = ptr[8];
m_c[2] = ptr[9];
m_c[3] = ptr[6];
}
else
{
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
m_c[3] = 0.0f;
}
}
/// <summary>Computes exponential of mv up to 12th term.
///
/// </summary>
public static mv exp(mv x)
{
return exp(x, 12);
}
/// <summary>
/// Constructs a new circle from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public circle(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new circle from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public circle(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new normalizedPoint from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public normalizedPoint(mv A /*, int filler */)
{
Set(A);
}
/// <summary>sets this to multivector value.
/// </summary>
public void Set(mv src)
{
AllocateGroups(src.gu());
if (m_c[0] != null) {
c3ga.Copy_1(m_c[0], src.m_c[0]);
}
if (m_c[1] != null) {
c3ga.Copy_5(m_c[1], src.m_c[1]);
}
if (m_c[2] != null) {
c3ga.Copy_10(m_c[2], src.m_c[2]);
}
if (m_c[3] != null) {
c3ga.Copy_10(m_c[3], src.m_c[3]);
}
if (m_c[4] != null) {
c3ga.Copy_5(m_c[4], src.m_c[4]);
}
if (m_c[5] != null) {
c3ga.Copy_1(m_c[5], src.m_c[5]);
}
}
/// <summary>
/// Constructs a new pointPair from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public pointPair(mv A /*, int filler */)
{
Set(A);
}
public void Set(mv src)
{
}
/// <summary>
/// Constructs a new line from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public line(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Copy constructor.
/// </summary>
public mv(mv A)
{
Set(A);
}
/// <summary>
/// Constructs a new dualLine from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public dualLine(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new plane from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public plane(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new line from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public line(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new flatPoint from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public flatPoint(mv A /*, int filler */)
{
Set(A);
}
public void Set(mv src)
{
if (src.c()[2] != null) {
float[] ptr = src.c()[2];
m_c[0] = ptr[7];
m_c[1] = ptr[8];
m_c[2] = ptr[9];
m_c[3] = ptr[6];
}
else {
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
m_c[3] = 0.0f;
}
}
/// <summary>Computes exponential of mv.
///
/// </summary>
public static mv exp(mv x, int order)
{
{ // First try special cases: check if (x * x) is scalar
mv xSquared = gp(x, x);
float s_xSquared = xSquared.get_scalar();
if ((norm2_returns_scalar(xSquared) - s_xSquared * s_xSquared) < 1E-06f) {
// OK (x * x == ~scalar), so use special cases:
if (s_xSquared < 0.0f) {
float a = (float)Math.Sqrt(-s_xSquared);
return sas(x, (float)Math.Sin(a) / a, (float)Math.Cos(a));
}
else if (s_xSquared > 0.0f) {
float a = (float)Math.Sqrt(s_xSquared);
return sas(x, (float)Math.Sinh(a) / a, (float)Math.Cosh(a));
}
else {
return sas(x, 1.0f, 1.0f);
}
}
}
// else do general series eval . . .
// result = 1 + ....
mv result = new mv(1.0f);
if (order == 0) return result;
// find scale (power of 2) such that its norm is < 1
ulong maxC = (ulong)x.LargestCoordinate();
int scale = 1;
if (maxC > 1) scale <<= 1;
while (maxC != 0)
{
maxC >>= 1;
scale <<= 1;
}
// scale
mv xScaled = gp(x, 1.0f / (float)scale);
// taylor series approximation
mv xPow1 = new mv(1.0f);
for (int i = 1; i <= order; i++) {
mv xPow2 = gp(xPow1, xScaled);
xPow1 = gp(xPow2, 1.0f / (float)i);
result = add(result, xPow1); // result2 = result1 + xPow1
}
// undo scaling
while (scale > 1)
{
result = gp(result, result);
scale >>= 1;
}
return result;
}
private mv Parse()
{
int token;
bool firstLoop = true;
// get the first token
token = getNextToken();
while (true) {
// reset for next basis blade
BasisBlade bb = new BasisBlade();
bool beDone = false; // basis element done
if (token == T_END_OF_STRING) break;
int cnt = 0;
while ((token == T_PLUS) || (token == T_MINUS)) { // accept all +-
cnt++;
startIdx = endIdx+1;
if (token == T_MINUS) bb.multiply(-1.0f); // -
token = getNextToken();
}
// require at least one +- if this is not the first term:
if ((!firstLoop) && (cnt == 0)) {
throw GetException("Expected '+' or '-'");
}
if ((token == T_NUMBER) ||
((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))) // must be number or basis vector
{
if (token == T_NUMBER) {
{ // multiply scale with value of number
try {
bb.multiply((float)Double.Parse(substring(startIdx, endIdx)));
} catch (Exception ) {
throw GetException("Cannot parse number");
}
}
startIdx = endIdx+1;
// * or ^ ?
token = getNextToken();
if ((token == T_WEDGE) || (token == T_MUL)) {
startIdx = endIdx+1;
// must find basis vector
token = getNextToken();
}
else { // just a single scalar is OK
startIdx = endIdx+1;
beDone = true;
}
}
if (!beDone) {
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR)) {
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx+1;
}
else {
throw GetException("Expected basis vector");
}
}
if (!beDone) {
// accept ^ basis vector as many times as it takes
while (true) {
// ^
token = getNextToken();
if (token != T_WEDGE) break;
startIdx = endIdx+1;
// basis vector
token = getNextToken();
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR)) {
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx+1;
}
else {
throw GetException("Expected basis vector");
}
}
}
} // end of 'if number or bv'
else if (token == T_BAD_CHARACTER) {
throw GetException("Bad character");
}
else if (token == T_BAD_NUMBER) {
throw GetException("Bad number");
}
else if (token == T_BAD_IDENTIFIER) {
throw GetException("Bad identifier");
}
else {
throw GetException("Unexpected token");
}
// add
sum(bb);
// remember that the first loop is done
firstLoop = false;
}
mv result = new mv(GroupBitmap.GRADE_0 | GroupBitmap.GRADE_1 | GroupBitmap.GRADE_2 | GroupBitmap.GRADE_3 | GroupBitmap.GRADE_4 | GroupBitmap.GRADE_5 | 0, coord);
result.Compress(0.0f);
return result;
}
/// <summary>
/// Constructs a new pointPair from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public pointPair(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new e1_t from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public e1_t(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new vectorE3GA from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public vectorE3GA(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Copy constructor.
/// </summary>
public mv(mv A)
{
Set(A);
}
public void Set(mv src)
{
}
public void Set(mv src)
{
if (src.c()[1] != null) {
float[] ptr = src.c()[1];
m_c[0] = ptr[1];
m_c[1] = ptr[2];
m_c[2] = ptr[3];
}
else {
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
}
}
private mv Parse()
{
int token;
bool firstLoop = true;
// get the first token
token = getNextToken();
while (true)
{
// reset for next basis blade
BasisBlade bb = new BasisBlade();
bool beDone = false; // basis element done
if (token == T_END_OF_STRING)
{
break;
}
int cnt = 0;
while ((token == T_PLUS) || (token == T_MINUS)) // accept all +-
{
cnt++;
startIdx = endIdx + 1;
if (token == T_MINUS)
{
bb.multiply(-1.0f); // -
}
token = getNextToken();
}
// require at least one +- if this is not the first term:
if ((!firstLoop) && (cnt == 0))
{
throw GetException("Expected '+' or '-'");
}
if ((token == T_NUMBER) ||
((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))) // must be number or basis vector
{
if (token == T_NUMBER)
{
{ // multiply scale with value of number
try {
bb.multiply((float)Double.Parse(substring(startIdx, endIdx)));
} catch (Exception) {
throw GetException("Cannot parse number");
}
}
startIdx = endIdx + 1;
// * or ^ ?
token = getNextToken();
if ((token == T_WEDGE) || (token == T_MUL))
{
startIdx = endIdx + 1;
// must find basis vector
token = getNextToken();
}
else // just a single scalar is OK
{
startIdx = endIdx + 1;
beDone = true;
}
}
if (!beDone)
{
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))
{
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx + 1;
}
else
{
throw GetException("Expected basis vector");
}
}
if (!beDone)
{
// accept ^ basis vector as many times as it takes
while (true)
{
// ^
token = getNextToken();
if (token != T_WEDGE)
{
break;
}
startIdx = endIdx + 1;
// basis vector
token = getNextToken();
if ((token >= T_FIRST_BASIS_VECTOR) && (token <= T_LAST_BASIS_VECTOR))
{
int bvIdx = token - T_FIRST_BASIS_VECTOR;
bb.wedgeBasisVector(bvIdx);
startIdx = endIdx + 1;
}
else
{
throw GetException("Expected basis vector");
}
}
}
} // end of 'if number or bv'
else if (token == T_BAD_CHARACTER)
{
throw GetException("Bad character");
}
else if (token == T_BAD_NUMBER)
{
throw GetException("Bad number");
}
else if (token == T_BAD_IDENTIFIER)
{
throw GetException("Bad identifier");
}
else
{
throw GetException("Unexpected token");
}
// add
sum(bb);
// remember that the first loop is done
firstLoop = false;
}
mv result = new mv(GroupBitmap.GRADE_0 | GroupBitmap.GRADE_1 | GroupBitmap.GRADE_2 | GroupBitmap.GRADE_3 | GroupBitmap.GRADE_4 | GroupBitmap.GRADE_5 | 0, coord);
result.Compress(0.0f);
return(result);
} // end of Parse()
/// <summary>
/// Constructs a new normalizedPoint from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public normalizedPoint(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new vectorE3GA from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public vectorE3GA(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new ni_t from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public ni_t(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new dualLine from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public dualLine(mv A /*, int filler */)
{
Set(A);
}
/// <summary>
/// Constructs a new flatPoint from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public flatPoint(mv A /*, int filler */)
{
Set(A);
}
/// <summary>internal conversion function
/// </summary>
public static float norm_returns_scalar(mv a)
{
return norm(a);
}
public void Set(mv src)
{
if (src.c()[3] != null) {
float[] ptr = src.c()[3];
m_c[0] = ptr[0];
m_c[1] = ptr[1];
m_c[2] = ptr[2];
m_c[3] = ptr[3];
m_c[4] = ptr[4];
m_c[5] = ptr[5];
m_c[6] = ptr[6];
m_c[7] = ptr[7];
m_c[8] = ptr[8];
m_c[9] = ptr[9];
}
else {
m_c[0] = 0.0f;
m_c[1] = 0.0f;
m_c[2] = 0.0f;
m_c[3] = 0.0f;
m_c[4] = 0.0f;
m_c[5] = 0.0f;
m_c[6] = 0.0f;
m_c[7] = 0.0f;
m_c[8] = 0.0f;
m_c[9] = 0.0f;
}
}
/// <summary>
/// Constructs a new plane from mv.
/// </summary>
/// <param name="A">The value to copy. Coordinates that cannot be represented are silently dropped. </param>
public plane(mv A /*, int filler */)
{
Set(A);
}