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/*
* Grid.cpp
*
* Created on: 18 Nov 2016
* Author: David
*/
#include "Grid.h"
#include <Platform/Platform.h>
#include <Platform/RepRap.h>
#include <GCodes/GCodes.h>
#include <Storage/FileStore.h>
#include <Math/Deviation.h>
#include <cmath>
#if SUPPORT_OBJECT_MODEL
// Object model table and functions
// Note: if using GCC version 7.3.1 20180622 and lambda functions are used in this table, you must compile this file with option -std=gnu++17.
// Otherwise the table will be allocated in RAM instead of flash, which wastes too much RAM.
// Macro to build a standard lambda function that includes the necessary type conversions
#define OBJECT_MODEL_FUNC(...) OBJECT_MODEL_FUNC_BODY(GridDefinition, __VA_ARGS__)
#define OBJECT_MODEL_FUNC_IF(...) OBJECT_MODEL_FUNC_IF_BODY(GridDefinition, __VA_ARGS__)
static constexpr ObjectModelArrayDescriptor axisArrayDescriptor =
{
nullptr, // no lock needed
[] (const ObjectModel *self, const ObjectExplorationContext&) noexcept -> size_t { return 2; },
[] (const ObjectModel *self, ObjectExplorationContext& context) noexcept -> ExpressionValue { return ExpressionValue(((const GridDefinition*)self)->GetAxisLetter(context.GetLastIndex())); }
};
static constexpr ObjectModelArrayDescriptor maxsArrayDescriptor =
{
nullptr, // no lock needed
[] (const ObjectModel *self, const ObjectExplorationContext&) noexcept -> size_t { return 2; },
[] (const ObjectModel *self, ObjectExplorationContext& context) noexcept -> ExpressionValue { return ExpressionValue(((const GridDefinition*)self)->GetMax(context.GetLastIndex()), 1); }
};
static constexpr ObjectModelArrayDescriptor minsArrayDescriptor =
{
nullptr, // no lock needed
[] (const ObjectModel *self, const ObjectExplorationContext&) noexcept -> size_t { return 2; },
[] (const ObjectModel *self, ObjectExplorationContext& context) noexcept -> ExpressionValue { return ExpressionValue(((const GridDefinition*)self)->GetMin(context.GetLastIndex()), 1); }
};
static constexpr ObjectModelArrayDescriptor spacingsArrayDescriptor =
{
nullptr, // no lock needed
[] (const ObjectModel *self, const ObjectExplorationContext&) noexcept -> size_t { return 2; },
[] (const ObjectModel *self, ObjectExplorationContext& context) noexcept -> ExpressionValue { return ExpressionValue(((const GridDefinition*)self)->GetSpacing(context.GetLastIndex()), 1); }
};
constexpr ObjectModelTableEntry GridDefinition::objectModelTable[] =
{
// Within each group, these entries must be in alphabetical order
// 0. GridDefinition members
{ "axes", OBJECT_MODEL_FUNC_NOSELF(&axisArrayDescriptor), ObjectModelEntryFlags::none },
{ "maxs", OBJECT_MODEL_FUNC_NOSELF(&maxsArrayDescriptor), ObjectModelEntryFlags::none },
{ "mins", OBJECT_MODEL_FUNC_NOSELF(&minsArrayDescriptor), ObjectModelEntryFlags::none },
{ "radius", OBJECT_MODEL_FUNC(self->radius, 1), ObjectModelEntryFlags::none },
{ "spacings", OBJECT_MODEL_FUNC_NOSELF(&spacingsArrayDescriptor), ObjectModelEntryFlags::none },
{ "xMax", OBJECT_MODEL_FUNC(self->maxs[0], 1), ObjectModelEntryFlags::obsolete },
{ "xMin", OBJECT_MODEL_FUNC(self->mins[0], 1), ObjectModelEntryFlags::obsolete },
{ "xSpacing", OBJECT_MODEL_FUNC(self->spacings[0], 1), ObjectModelEntryFlags::obsolete },
{ "yMax", OBJECT_MODEL_FUNC(self->maxs[1], 1), ObjectModelEntryFlags::obsolete },
{ "yMin", OBJECT_MODEL_FUNC(self->mins[1], 1), ObjectModelEntryFlags::obsolete },
{ "ySpacing", OBJECT_MODEL_FUNC(self->spacings[1], 1), ObjectModelEntryFlags::obsolete },
};
constexpr uint8_t GridDefinition::objectModelTableDescriptor[] = { 1, 11 };
DEFINE_GET_OBJECT_MODEL_TABLE(GridDefinition)
#endif
const char * const GridDefinition::HeightMapLabelLines[] =
{
"xmin,xmax,ymin,ymax,radius,spacing,xnum,ynum", // old version label line
"xmin,xmax,ymin,ymax,radius,xspacing,yspacing,xnum,ynum", // label line until 3.3-beta1
"axis0,axis1,min0,max0,min1,max1,radius,spacing0,spacing1,num0,num1", // label line from 3.3-beta2
};
// Initialise the grid to be invalid
GridDefinition::GridDefinition() noexcept : radius(-1.0), isValid(false)
{
letters[0] = 'X';
letters[1] = 'Y';
mins[0] = mins[1] = 0.0;
maxs[0] = maxs[1] = -1.0;
spacings[0] = spacings[1] = 0.0;
nums[0] = nums[1] = 0;
recipAxisSpacings[0] = recipAxisSpacings[1] = 0.0;
}
// Set the grid parameters ands return true if it is now valid
bool GridDefinition::Set(const char axisLetters[2], const float axis0Range[2], const float axis1Range[2], float pRadius, const float pSpacings[2]) noexcept
{
letters[0] = axisLetters[0];
letters[1] = axisLetters[1];
mins[0] = axis0Range[0];
maxs[0] = axis0Range[1];
mins[1] = axis1Range[0];
maxs[1] = axis1Range[1];
radius = pRadius;
spacings[0] = pSpacings[0];
spacings[1] = pSpacings[1];
CheckValidity(true);
return isValid;
}
// Set up internal variables and check validity of the grid.
// If setNum0Num1 is true then set up numAxis0 and numAxis1, otherwise leave them alone if the grid is valid
// If the grid is valid then set up recipAxis0spacing and recipAxis1spacing
void GridDefinition::CheckValidity(bool setNum0Num1) noexcept
{
if (maxs[0] - mins[0] < MinRange || spacings[0] < MinSpacing || maxs[1] - mins[1] < MinRange || spacings[1] < MinSpacing)
{
isValid = false;
if (setNum0Num1)
{
nums[0] = nums[1] = 0;
}
}
else
{
if (setNum0Num1)
{
nums[0] = (uint32_t)((maxs[0] - mins[0])/spacings[0]) + 1;
nums[1] = (uint32_t)((maxs[1] - mins[1])/spacings[1]) + 1;
}
const size_t axis0NumForLetter = reprap.GetGCodes().GetAxisNumberForLetter(letters[0]);
const size_t axis1NumForLetter = reprap.GetGCodes().GetAxisNumberForLetter(letters[1]);
const size_t numVisibleAxes = reprap.GetGCodes().GetVisibleAxes();
isValid = NumPoints() != 0 && NumPoints() <= MaxGridProbePoints
&& (radius < 0.0 || radius >= 1.0)
&& nums[0] <= MaxAxis0GridPoints
&& letters[0] != letters[1]
&& axis0NumForLetter < numVisibleAxes
&& axis1NumForLetter < numVisibleAxes;
if (isValid)
{
axisNumbers[0] = axis0NumForLetter;
axisNumbers[1] = axis1NumForLetter;
recipAxisSpacings[0] = 1.0/spacings[0];
recipAxisSpacings[1] = 1.0/spacings[1];
}
}
}
bool GridDefinition::IsInRadius(float axis0, float y) const noexcept
{
return radius < 0.0 || fsquare(axis0) + fsquare(y) < fsquare(radius);
}
// Append the grid parameters to the end of a string
void GridDefinition::PrintParameters(const StringRef& s) const noexcept
{
s.catf("%c%.1f:%.1f, %c%.1f:%.1f, radius %.1f, %c spacing %.1f, %c spacing %.1f, %" PRIu32 " points",
letters[0], (double)mins[0], (double)maxs[0], letters[1], (double)mins[1], (double)maxs[1], (double)radius, letters[0], (double)spacings[0], letters[1], (double)spacings[1], NumPoints());
}
// Write the parameter label line to a string
void GridDefinition::WriteHeadingAndParameters(const StringRef& s) const noexcept
{
s.printf("%s\n%c,%c,%.2f,%.2f,%.2f,%.2f,%.2f,%.2f,%.2f,%" PRIi32 ",%" PRIi32 "\n",
HeightMapLabelLines[ARRAY_UPB(HeightMapLabelLines)], letters[0], letters[1], (double)mins[0], (double)maxs[0], (double)mins[1], (double)maxs[1], (double)radius, (double)spacings[0], (double)spacings[1], nums[0], nums[1]);
}
// Check the parameter label line, returning -1 if not recognised, else the version we found
/*static*/ int GridDefinition::CheckHeading(const StringRef& s) noexcept
{
for (size_t i = 0; i < ARRAY_SIZE(HeightMapLabelLines); ++i)
{
if (StringStartsWith(s.c_str(), HeightMapLabelLines[i]))
{
return (int)i;
}
}
return -1;
}
// Read the grid parameters from a string returning true if success
bool GridDefinition::ReadParameters(const StringRef& s, int version) noexcept
{
// 2018-04-08: rewrote this not to use sscanf because that function isn't thread safe
isValid = false; // assume failure
const char *p = s.c_str();
const char *q;
if (version < 2)
{
letters[0] = 'X';
letters[1] = 'Y';
}
else
{
letters[0] = *p;
++p;
if (*p != ',')
{
return false;
}
++p;
letters[1] = *p;
++p;
if (*p != ',')
{
return false;
}
++p;
}
mins[0] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
maxs[0] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
mins[1] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
maxs[1] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
radius = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
spacings[0] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
if (version == 0)
{
spacings[1] = spacings[0];
}
else
{
spacings[1] = SafeStrtof(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
}
nums[0] = StrToU32(p, &q);
if (p == q || *q != ',')
{
return false;
}
p = q + 1;
nums[1] = StrToU32(p, &q);
if (p == q)
{
return false;
}
CheckValidity(false);
return true;
}
// Print what is wrong with the grid, appending it to the existing string
void GridDefinition::PrintError(float originalAxis0range, float originalAxis1range, const StringRef& r) const noexcept
{
if (spacings[0] < MinSpacing || spacings[1] < MinSpacing)
{
r.cat("Spacing too small");
}
else if (nums[0] == 0)
{
r.catf("%c range too small", letters[0]);
}
else if (nums[1] == 0)
{
r.catf("%c range too small", letters[1]);
}
else if ( nums[0] > MaxAxis0GridPoints
|| nums[0] > MaxGridProbePoints || nums[1] > MaxGridProbePoints // check X and Y individually in case X*Y overflows
|| NumPoints() > MaxGridProbePoints
)
{
const float totalRange = originalAxis0range + originalAxis1range;
const float area = originalAxis0range * originalAxis1range;
const float minSpacing = (totalRange + fastSqrtf(fsquare(totalRange) + 4.0 * (MaxGridProbePoints - 1) * area))/(2.0 * (MaxGridProbePoints - 1));
const float minXspacing = originalAxis0range/(MaxAxis0GridPoints - 1);
r.catf("Too many grid points; suggest increase spacing to %.1fmm", (double)max<float>(minSpacing, minXspacing));
}
else
{
// The only thing left is a bad radius
r.cat("Bad radius");
}
}
// Increase the version number in the following string whenever we change the format of the height map file significantly.
// Adding more fields to the header row can be handled in GridDefinition::ReadParameters(), though.
const char * const HeightMap::HeightMapComment = "RepRapFirmware height map file v2";
HeightMap::HeightMap() noexcept : useMap(false) { }
void HeightMap::SetGrid(const GridDefinition& gd) noexcept
{
useMap = false;
def = gd;
ClearGridHeights();
}
void HeightMap::ClearGridHeights() noexcept
{
gridHeightSet.ClearAll();
#if HAS_MASS_STORAGE
fileName.Clear();
#endif
}
// Set the height of a grid point
void HeightMap::SetGridHeight(size_t axis0Index, size_t axis1Index, float height) noexcept
{
SetGridHeight(axis1Index * def.nums[0] + axis0Index, height);
}
void HeightMap::SetGridHeight(size_t index, float height) noexcept
{
if (index < MaxGridProbePoints)
{
gridHeights[index] = height;
gridHeightSet.SetBit(index);
}
}
// Return the minimum number of segments for a move by this X or Y amount
// Note that deltaAxis0 and deltaAxis1 may be negative
unsigned int HeightMap::GetMinimumSegments(float deltaAxis0, float deltaAxis1) const noexcept
{
const float axis0Distance = fabsf(deltaAxis0);
unsigned int axis0Segments = (axis0Distance > 0.0) ? (unsigned int)(axis0Distance * def.recipAxisSpacings[0] + 0.4) : 1;
const float axis1Distance = fabsf(deltaAxis1);
unsigned int axis1Segments = (axis1Distance > 0.0) ? (unsigned int)(axis1Distance * def.recipAxisSpacings[1] + 0.4) : 1;
return max<unsigned int>(axis0Segments, axis1Segments);
}
#if HAS_MASS_STORAGE
// Save the grid to file returning true if an error occurred
bool HeightMap::SaveToFile(FileStore *f, const char *fname, float zOffset) noexcept
{
String<StringLength500> bufferSpace;
const StringRef buf = bufferSpace.GetRef();
// Write the header comment
buf.copy(HeightMapComment);
tm timeInfo;
if (reprap.GetPlatform().GetDateTime(timeInfo))
{
buf.catf(" generated at %04u-%02u-%02u %02u:%02u",
timeInfo.tm_year + 1900, timeInfo.tm_mon + 1, timeInfo.tm_mday, timeInfo.tm_hour, timeInfo.tm_min);
}
Deviation deviation;
float minError, maxError;
(void)GetStatistics(deviation, minError, maxError);
buf.catf(", min error %.3f, max error %.3f, mean %.3f, deviation %.3f\n",
(double)(minError + zOffset), (double)(maxError + zOffset), (double)(deviation.GetMean() + zOffset), (double)deviation.GetDeviationFromMean());
if (!f->Write(buf.c_str()))
{
return true;
}
// Write the grid parameters
def.WriteHeadingAndParameters(buf);
if (!f->Write(buf.c_str()))
{
return true;
}
// Write the grid heights. We use a fixed field with of 6 characters to make is easier to view.
uint32_t index = 0;
for (uint32_t i = 0; i < def.nums[1]; ++i)
{
buf.Clear();
for (uint32_t j = 0; j < def.nums[0]; ++j)
{
if (j != 0)
{
buf.cat(',');
}
if (gridHeightSet.IsBitSet(index))
{
buf.catf("%7.3f", (double)(gridHeights[index] + zOffset));
}
else
{
buf.cat(" 0"); // write 0 with no decimal point where we didn't probe, so we can tell when we reload it
}
++index;
}
buf.cat('\n');
if (!f->Write(buf.c_str()))
{
return true;
}
}
fileName.copy(fname);
return false;
}
// Load the grid from file, returning true if an error occurred with the error reason appended to the buffer
bool HeightMap::LoadFromFile(FileStore *f, const char *fname, const StringRef& r) noexcept
{
const size_t MaxLineLength = (MaxAxis0GridPoints * 8) + 2; // maximum length of a line in the height map file, need 8 characters per grid point
const char* const readFailureText = "failed to read line from file";
char buffer[MaxLineLength + 1];
StringRef s(buffer, ARRAY_SIZE(buffer));
ClearGridHeights(); // this also clears the filename
GridDefinition newGrid;
int gridVersion;
if (f->ReadLine(buffer, sizeof(buffer)) <= 0)
{
r.cat(readFailureText);
}
else if (!StringStartsWith(buffer, HeightMapComment)) // check the version line is as expected
{
r.cat("bad header line or wrong version header");
}
else if (f->ReadLine(buffer, sizeof(buffer)) <= 0)
{
r.cat(readFailureText);
}
else if ((gridVersion = GridDefinition::CheckHeading(s)) < 0) // check the label line is as expected
{
r.cat("bad label line");
}
else if (f->ReadLine(buffer, sizeof(buffer)) <= 0) // read the height map parameters
{
r.cat(readFailureText);
}
else if (!newGrid.ReadParameters(s, gridVersion))
{
r.cat("failed to parse grid parameters");
}
else if (!newGrid.IsValid())
{
r.cat("invalid grid");
}
else
{
SetGrid(newGrid);
for (uint32_t row = 0; row < def.nums[1]; ++row) // read the grid a row at a time
{
if (f->ReadLine(buffer, sizeof(buffer)) <= 0)
{
r.cat(readFailureText);
return true; // failed to read a line
}
const char *p = buffer;
for (uint32_t col = 0; col < def.nums[0]; ++col)
{
while (*p == ' ' || *p == '\t')
{
++p;
}
if (*p == '0' && (p[1] == ',' || p[1] == 0))
{
// Values of 0 with no decimal places in un-probed values, so leave the point set as not valid
++p;
}
else
{
const char* np;
const float f = SafeStrtof(p, &np);
if (np == p)
{
r.catf("number expected at line %" PRIu32 " column %d", row + 3, (p - buffer) + 1);
return true; // failed to read a number
}
SetGridHeight(col, row, f);
p = np;
}
if (*p == ',')
{
++p;
}
}
}
ExtrapolateMissing();
fileName.copy(fname);
return false; // success!
}
return true; // an error occurred
}
#endif
#if HAS_SBC_INTERFACE
// Update the filename
void HeightMap::SetFileName(const char *name) noexcept
{
fileName.copy(name);
}
// Save the grid to a sequential array in the same way as to a regular CSV file
void HeightMap::SaveToArray(float *arr, float zOffset) const noexcept
{
size_t index = 0;
for (size_t i = 0; i < def.nums[1]; ++i)
{
for (size_t j = 0; j < def.nums[0]; ++j)
{
arr[index] = gridHeightSet.IsBitSet(index) ? (gridHeights[index] + zOffset) : std::numeric_limits<float>::quiet_NaN();
index++;
}
}
}
#endif
// Return number of points probed, mean and RMS deviation, min and max error
unsigned int HeightMap::GetStatistics(Deviation& deviation, float& minError, float& maxError) const noexcept
{
double heightSum = 0.0, heightSquaredSum = 0.0;
minError = 9999.0;
maxError = -9999.0;
unsigned int numProbed = 0;
for (uint32_t i = 0; i < def.NumPoints(); ++i)
{
if (gridHeightSet.IsBitSet(i))
{
++numProbed;
const float fHeightError = gridHeights[i];
if (fHeightError > maxError)
{
maxError = fHeightError;
}
if (fHeightError < minError)
{
minError = fHeightError;
}
const double dHeightError = (double)fHeightError;
heightSum += dHeightError;
heightSquaredSum += dsquare(dHeightError);
}
}
deviation.Set(heightSquaredSum, heightSum, numProbed);
return numProbed;
}
// Try to turn mesh compensation on or off and report the state achieved
bool HeightMap::UseHeightMap(bool b) noexcept
{
useMap = b && def.IsValid();
return useMap;
}
// Compute the height error at the specified point
float HeightMap::GetInterpolatedHeightError(float axis0, float axis1) const noexcept
{
if (!useMap)
{
return 0.0;
}
// Last grid point
const float xLast = def.mins[0] + (def.nums[0]-1)*def.spacings[0];
const float yLast = def.mins[1] + (def.nums[1]-1)*def.spacings[1];
// Clamp to rectangle so InterpolateXY will always have valid parameters
const float fEPSILON = 0.01;
if (axis0 < def.mins[0]) { axis0 = def.mins[0]; }
if (axis1 < def.mins[1]) { axis1 = def.mins[1]; }
if (axis0 > xLast -fEPSILON) { axis0 = xLast -fEPSILON; }
if (axis1 > yLast -fEPSILON) { axis1 = yLast -fEPSILON; }
const float xf = (axis0 - def.mins[0]) * def.recipAxisSpacings[0];
const float xFloor = floor(xf);
const int32_t xIndex = (int32_t)xFloor;
const float yf = (axis1 - def.mins[1]) * def.recipAxisSpacings[1];
const float yFloor = floor(yf);
const int32_t yIndex = (int32_t)yFloor;
return InterpolateAxis0Axis1(xIndex, yIndex, xf - xFloor, yf - yFloor);
}
float HeightMap::InterpolateAxis0Axis1(uint32_t axis0Index, uint32_t axis1Index, float axis0Frac, float axis1Frac) const noexcept
{
const uint32_t indexX0Y0 = GetMapIndex(axis0Index, axis1Index); // (X0,Y0)
const uint32_t indexX1Y0 = indexX0Y0 + 1; // (X1,Y0)
const uint32_t indexX0Y1 = indexX0Y0 + def.nums[0]; // (X0 Y1)
const uint32_t indexX1Y1 = indexX0Y1 + 1; // (X1,Y1)
const float xyFrac = axis0Frac * axis1Frac;
return (gridHeights[indexX0Y0] * (1.0 - axis0Frac - axis1Frac + xyFrac))
+ (gridHeights[indexX1Y0] * (axis0Frac - xyFrac))
+ (gridHeights[indexX0Y1] * (axis1Frac - xyFrac))
+ (gridHeights[indexX1Y1] * xyFrac);
}
void HeightMap::ExtrapolateMissing() noexcept
{
//1: calculating the bed plane by least squares fit
//2: filling in missing points
//algorithm: http://www.ilikebigbits.com/blog/2015/3/2/plane-from-points
float sumAxis0 = 0, sumAxis1 = 0, sumZ = 0;
int n = 0;
for (uint32_t iAxis1 = 0; iAxis1 < def.nums[1]; iAxis1++)
{
for (uint32_t iAxis0 = 0; iAxis0 < def.nums[0]; iAxis0++)
{
const uint32_t index = GetMapIndex(iAxis0, iAxis1);
if (gridHeightSet.IsBitSet(index))
{
const float fAxis0 = (def.spacings[0] * iAxis0) + def.mins[0];
const float fAxis1 = (def.spacings[1] * iAxis1) + def.mins[1];
const float fZ = gridHeights[index];
n++;
sumAxis0 += fAxis0; sumAxis1 += fAxis1; sumZ += fZ;
}
}
}
const float invN = 1.0 / float(n);
const float centAxis0 = sumAxis0 * invN, centAxis1 = sumAxis1 * invN, centZ = sumZ * invN;
// Calculate full 3x3 covariance matrix, excluding symmetries
float axis0Axis0 = 0.0; float axis0Axis1 = 0.0; float axis0z = 0.0;
float axis1Axis1 = 0.0; float axis1z = 0.0; float zz = 0.0;
for (uint32_t iAxis1 = 0; iAxis1 < def.nums[1]; iAxis1++)
{
for (uint32_t iAxis0 = 0; iAxis0 < def.nums[0]; iAxis0++)
{
const uint32_t index = GetMapIndex(iAxis0, iAxis1);
if (gridHeightSet.IsBitSet(index))
{
const float fAxis0 = (def.spacings[0] * iAxis0) + def.mins[0];
const float fAxis1 = (def.spacings[1] * iAxis1) + def.mins[1];
const float fZ = gridHeights[index];
const float rAxis0 = fAxis0 - centAxis0;
const float rAxis1 = fAxis1 - centAxis1;
const float rZ = fZ - centZ;
axis0Axis0 += rAxis0 * rAxis0;
axis0Axis1 += rAxis0 * rAxis1;
axis0z += rAxis0 * rZ;
axis1Axis1 += rAxis1 * rAxis1;
axis1z += rAxis1 * rZ;
zz += rZ * rZ;
}
}
}
const float detZ = axis0Axis0*axis1Axis1 - axis0Axis1*axis0Axis1;
if (detZ <= 0)
{
// Not a valid plane (or a vertical one)
return;
}
// Plane equation: ax+by+cz=d -> z = (d-(ax+by))/c
float a = (axis1z*axis0Axis1 - axis0z*axis1Axis1) / detZ;
float b = (axis0z*axis0Axis1 - axis1z*axis0Axis0) / detZ;
const float invC = fastSqrtf(a*a + b*b + 1.0);
const float normLenInv = 1.0 / invC;
a *= normLenInv;
b *= normLenInv;
const float c = normLenInv;
const float d = centAxis0*a + centAxis1*b + centZ*c;
// Fill in the blanks
for (uint32_t iAxis1 = 0; iAxis1 < def.nums[1]; iAxis1++)
{
for (uint32_t iAxis0 = 0; iAxis0 < def.nums[0]; iAxis0++)
{
const uint32_t index = GetMapIndex(iAxis0, iAxis1);
if (!gridHeightSet.IsBitSet(index))
{
const float fAxis0 = (def.spacings[0] * iAxis0) + def.mins[0];
const float fAxis1 = (def.spacings[1] * iAxis1) + def.mins[1];
const float fZ = (d - (a * fAxis0 + b * fAxis1)) * invC;
gridHeights[index] = fZ; // fill in Z but don't mark it as set so we can always differentiate between measured and extrapolated
}
}
}
}
// End
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