Detailed Description

Class containing interpolation and easing functions optimized for fixed-point arithmetic.

This class provides a comprehensive set of interpolation and easing functions designed for game development. All functions are implemented using fixed-point arithmetic for consistent behavior across platforms.

Key features:

Compile-time evaluation with constexpr
No floating-point operations
Optimized for Saturn hardware
Memory-efficient implementations

#include <interpolation.hpp>

Static Public Member Functions
static constexpr Fxp	BounceEaseIn (const Fxp &start, const Fxp &end, const Fxp &t)
	Bounce ease-in interpolation for reverse bouncing ball effect.

static constexpr Fxp	BounceEaseOut (const Fxp &start, const Fxp &end, const Fxp &t)
	Bounce ease-out interpolation for bouncing ball effect.

static constexpr Fxp	Clamp (const Fxp &value, const Fxp &min, const Fxp &max)
	Clamps a value between minimum and maximum bounds.

static constexpr Fxp	CubicEaseIn (const Fxp &start, const Fxp &end, const Fxp &t)
	Cubic ease-in interpolation for stronger acceleration.

static constexpr Fxp	CubicEaseOut (const Fxp &start, const Fxp &end, const Fxp &t)
	Cubic ease-out interpolation for stronger deceleration.

static constexpr Fxp	EaseIn (const Fxp &start, const Fxp &end, const Fxp &t)
	Quadratic ease-in interpolation for accelerating motion.

static constexpr Fxp	EaseOut (const Fxp &start, const Fxp &end, const Fxp &t)
	Quadratic ease-out interpolation for decelerating motion.

static constexpr Fxp	ElasticEaseIn (const Fxp &start, const Fxp &end, const Fxp &t)
	Elastic ease-in interpolation for spring-like motion.

static constexpr Fxp	Lerp (const Fxp &start, const Fxp &end, const Fxp &t)
	Linear interpolation between two fixed-point values.

static constexpr Fxp	Smoothstep (const Fxp &start, const Fxp &end, const Fxp &t)
	Smoothstep interpolation for smooth acceleration and deceleration.

Member Function Documentation

◆ BounceEaseIn()

static constexpr Fxp SRL::Math::Interpolation::BounceEaseIn	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Bounce ease-in interpolation for reverse bouncing ball effect.

Implements bouncing by reversing BounceEaseOut. Creates a series of bounces that converge to the start.

The motion consists of four phases in reverse:

Small initial bounces (10% of time)
Medium bounce (18% of time)
Large bounce (36% of time)
Final launch (36% of time)

Common uses:

Object launches
UI element takeoffs
Character jump startup
Power-up activation

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: Reverses BounceEaseOut for symmetric animations

◆ BounceEaseOut()

static constexpr Fxp SRL::Math::Interpolation::BounceEaseOut	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Bounce ease-out interpolation for bouncing ball effect.

Implements bouncing using piecewise quadratic functions. Simulates diminishing bounces of an elastic ball.

The motion consists of four phases:

Initial fall (36% of time)
First bounce (36% of time)
Second bounce (18% of time)
Final small bounces (10% of time)

Common uses:

Dropping objects
UI element landings
Character jump landing
Button clicks

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: Each bounce is approximately 75% the height of previous

◆ Clamp()

static constexpr Fxp SRL::Math::Interpolation::Clamp	(	const Fxp &	value,
		const Fxp &	min,
		const Fxp &	max )

inlinestaticconstexpr

Clamps a value between minimum and maximum bounds.

Ensures a value stays within specified bounds using the formula: result = min(max(value, min), max)

Clamping behavior:

If value < min, returns min
If value > max, returns max
Otherwise, returns value unchanged

Common uses:

Constraining player movement
Limiting camera angles
Bounding UI element positions
Normalizing input values

Parameters

value	Value to be clamped
min	Minimum allowed value
max	Maximum allowed value

Returns: Clamped value

Note: Assumes min <= max

◆ CubicEaseIn()

static constexpr Fxp SRL::Math::Interpolation::CubicEaseIn	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Cubic ease-in interpolation for stronger acceleration.

Implements cubic easing using the formula: t³

The easing produces this motion:

Very slow start
Rapid acceleration
Maximum velocity at end

Common uses:

Dramatic entrances
Power-up effects
Explosion start
Heavy object movement

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: More pronounced than quadratic EaseIn

◆ CubicEaseOut()

static constexpr Fxp SRL::Math::Interpolation::CubicEaseOut	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Cubic ease-out interpolation for stronger deceleration.

Implements cubic easing using the formula: (t - 1)³ + 1

The easing produces this motion:

Maximum velocity at start
Rapid deceleration
Very slow end

Common uses:

Dramatic exits
Impact effects
Explosion end
Heavy object stopping

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: More pronounced than quadratic EaseOut

◆ EaseIn()

static constexpr Fxp SRL::Math::Interpolation::EaseIn	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Quadratic ease-in interpolation for accelerating motion.

Implements quadratic easing using the formula: t²

The easing produces this motion:

Starts slow (zero velocity)
Continuously accelerates
Reaches full velocity at end

Common uses:

Character movement startup
UI element entrance
Zoom-in effects
Power-up animations

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: For symmetric animation, pair with EaseOut

◆ EaseOut()

static constexpr Fxp SRL::Math::Interpolation::EaseOut	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Quadratic ease-out interpolation for decelerating motion.

Implements quadratic easing using the formula: -t * (t - 2)

The easing produces this motion:

Starts at full velocity
Continuously decelerates
Stops smoothly (zero velocity)

Common uses:

Character movement stop
UI element exit
Zoom-out effects
Landing animations

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: For symmetric animation, pair with EaseIn

◆ ElasticEaseIn()

static constexpr Fxp SRL::Math::Interpolation::ElasticEaseIn	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Elastic ease-in interpolation for spring-like motion.

Implements elastic easing with configurable period and amplitude. Uses quadratic approximation of sine for efficiency.

The easing produces this motion:

Multiple overshoots
Decreasing amplitude
Final snap to position

Common uses:

Menu bounces
Character stretching
Projectile charge-up
Spring animations

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Eased value

Note: Uses approximated sine to avoid trigonometric tables

◆ Lerp()

static constexpr Fxp SRL::Math::Interpolation::Lerp	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Linear interpolation between two fixed-point values.

Performs linear interpolation (lerp) between start and end values using the formula: result = start + (end - start) * t

The interpolation follows this pattern:

When t = 0, returns start
When t = 1, returns end
When t = 0.5, returns the midpoint

Common uses:

Camera movement
UI element transitions
Color blending
Position interpolation

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor in range [0,1]

Returns: Interpolated value

Note: For best performance, ensure t is pre-clamped to [0,1]

◆ Smoothstep()

static constexpr Fxp SRL::Math::Interpolation::Smoothstep	(	const Fxp &	start,
		const Fxp &	end,
		const Fxp &	t )

inlinestaticconstexpr

Smoothstep interpolation for smooth acceleration and deceleration.

Implements Ken Perlin's smoothstep function using the formula: 3t² - 2t³

The smoothstep produces this behavior:

Smooth acceleration from start
Constant velocity at midpoint
Smooth deceleration to end

Common uses:

Camera transitions
Smooth UI animations
Particle system parameters
Fade effects

Parameters

start	Starting value of the interpolation
end	Ending value of the interpolation
t	Interpolation factor, automatically clamped to [0,1]

Returns: Smoothly interpolated value

Note: Automatically clamps input t to [0,1] for safety

Detailed Description

Static Public Member Functions

Member Function Documentation

◆ BounceEaseIn()

◆ BounceEaseOut()

◆ Clamp()

◆ CubicEaseIn()

◆ CubicEaseOut()

◆ EaseIn()

◆ EaseOut()

◆ ElasticEaseIn()

◆ Lerp()

◆ Smoothstep()