table3d_interpolate.cpp File Reference

Support functions for 3D table interpolation. More...

#include "table3d_interpolate.h"
#include "maths.h"
#include "unit_testing.h"
#include "table2d.h"

Functions
Interpolation
TESTABLE_INLINE_STATIC QU1X8_t	compute_bin_position (const uint16_t &value, const table3d_bin_t &bin, const uint16_t &multiplier)
	Compute the % position of a value within a bin.
TESTABLE_INLINE_STATIC row_col2d	toTopRight (const table3d_bin_t &xBin, const table3d_bin_t &yBin, const table3d_dim_t &axisSize)
	Get the top right corner of the value coordinates in a 3D table, based on x/y axis coords.
static row_col2d	toBottomLeft (const row_col2d &topRight, const table3d_dim_t &axisSize)
	Get the bottom left corner of the value coordinates in a 3D table, based on top right corner.
TESTABLE_INLINE_STATIC table3d_value_t	bilinear_interpolation (const table3d_value_t &tl, const table3d_value_t &tr, const table3d_value_t &bl, const table3d_value_t &br, const QU1X8_t &dx, const QU1X8_t &dy)
	2d interpolation, given 4 corner values and x/y percentages
table3d_value_t	interpolate_3d_value (const xy_pair_t &lookUpValues, const table3d_dim_t &axisSize, const table3d_value_t *pValues, const table3d_bin_t &xBin, const uint16_t xMultiplier, const table3d_bin_t &yBin, const uint16_t yMultiplier)
	Interpolate a table value from axis bins & values.

Fixed point math
typedef uint16_t	QU1X8_t
	Unsigned fixed point number type with 1 integer bit & 8 fractional bits.
constexpr QU1X8_t	QU1X8_INTEGER_SHIFT = 8
	Integer shift to convert to/from QU1X8_t.
TESTABLE_CONSTEXPR QU1X8_t	QU1X8_ONE = toQU1X8(1U)
	Precomputed value of 1 in QU1X8_t.
TESTABLE_CONSTEXPR QU1X8_t	QU1X8_HALF = QU1X8_ONE/2U
	Precomputed value of 0.5 in QU1X8_t.
static constexpr QU1X8_t	toQU1X8 (uint16_t base)
	Unsigned fixed point number type with 1 integer bit & 8 fractional bits.
static constexpr uint16_t	fromQU1X8 (QU1X8_t base)
	Unsigned fixed point number type with 1 integer bit & 8 fractional bits.
TESTABLE_INLINE_STATIC QU1X8_t	mulQU1X8 (QU1X8_t a, QU1X8_t b)
	Multiply two QU1X8_t values.

Detailed Description

Support functions for 3D table interpolation.

Typedef Documentation

QU1X8_t

typedef uint16_t QU1X8_t

Unsigned fixed point number type with 1 integer bit & 8 fractional bits.

See also

https://en.wikipedia.org/wiki/Q_(number_format).

This is specialised for the number range 0..1 - a generic fixed point class would miss some important optimisations. Specifically, we can avoid type promotion during multiplication.

Function Documentation

bilinear_interpolation()

TESTABLE_INLINE_STATIC table3d_value_t bilinear_interpolation	(	const table3d_value_t &	tl,
		const table3d_value_t &	tr,
		const table3d_value_t &	bl,
		const table3d_value_t &	br,
		const QU1X8_t &	dx,
		const QU1X8_t &	dy
	)

2d interpolation, given 4 corner values and x/y percentages

 tl----------------tr
 |                 |
 |                 |
 |                 |
 |>>>>>dx>>>>?     |
 |           ^     |
 |           dy    |
 |           ^     |
 bl----------------br

Parameters

tl	Top left value
tr	Top right value
bl	Bottom left value
br	Bottom right value
dx	X distance
dy	Y distance

Returns

table3d_value_t

compute_bin_position()

TESTABLE_INLINE_STATIC QU1X8_t compute_bin_position	(	const uint16_t &	value,
		const table3d_bin_t &	bin,
		const uint16_t &	multiplier
	)

Compute the % position of a value within a bin.

• 0%==at/below the bin minimum
• 100%==at/above the bin maximum
• 50%==in the middle of the bin.

Note

The multiplier is used to scale the axis values to the same scale as the value being checked. This retains the full precision of the axis values, thus the computed position and eventually the final interpolated result

Parameters

value	The value to check.
bin	The axis bin.
multiplier	The multiplier for the axis values.

Returns

QU1X8_t The % position of the value within the bin.

fromQU1X8()

static constexpr uint16_t fromQU1X8 ( QU1X8_t  base )

staticconstexpr

Unsigned fixed point number type with 1 integer bit & 8 fractional bits.

See also

https://en.wikipedia.org/wiki/Q_(number_format).

This is specialised for the number range 0..1 - a generic fixed point class would miss some important optimisations. Specifically, we can avoid type promotion during multiplication.

interpolate_3d_value()

table3d_value_t interpolate_3d_value	(	const xy_pair_t &	lookUpValues,
		const table3d_dim_t &	axisSize,
		const table3d_value_t *	pValues,
		const table3d_bin_t &	xBin,
		const uint16_t	xMultiplier,
		const table3d_bin_t &	yBin,
		const uint16_t	yMultiplier
	)

Interpolate a table value from axis bins & values.

Parameters

lookUpValues	The x & y axis values we are interpolating
axisSize	The length of an axis
pValues	The interpolation source values
xBin	The x-axis bin containing lookUpValues.x
xMultiplier	The x-axis multiplier
yBin	The y-axis bin containing lookUpValues.y
yMultiplier	The y-axis multiplier

Returns

table3d_value_t

mulQU1X8()

TESTABLE_INLINE_STATIC QU1X8_t mulQU1X8	(	QU1X8_t	a,
		QU1X8_t	b
	)

Multiply two QU1X8_t values.

toBottomLeft()

static row_col2d toBottomLeft ( const row_col2d &  topRight, const table3d_dim_t &  axisSize  )

inlinestatic

Get the bottom left corner of the value coordinates in a 3D table, based on top right corner.

toQU1X8()

static constexpr QU1X8_t toQU1X8 ( uint16_t  base )

staticconstexpr

Unsigned fixed point number type with 1 integer bit & 8 fractional bits.

See also

https://en.wikipedia.org/wiki/Q_(number_format).

This is specialised for the number range 0..1 - a generic fixed point class would miss some important optimisations. Specifically, we can avoid type promotion during multiplication.

toTopRight()

TESTABLE_INLINE_STATIC row_col2d toTopRight	(	const table3d_bin_t &	xBin,
		const table3d_bin_t &	yBin,
		const table3d_dim_t &	axisSize
	)

Get the top right corner of the value coordinates in a 3D table, based on x/y axis coords.

Variable Documentation

QU1X8_HALF

TESTABLE_CONSTEXPR QU1X8_t QU1X8_HALF = QU1X8_ONE/2U

Precomputed value of 0.5 in QU1X8_t.

QU1X8_INTEGER_SHIFT

constexpr QU1X8_t QU1X8_INTEGER_SHIFT = 8

constexpr

Integer shift to convert to/from QU1X8_t.

QU1X8_ONE

TESTABLE_CONSTEXPR QU1X8_t QU1X8_ONE = toQU1X8(1U)

Precomputed value of 1 in QU1X8_t.