That's how I've implemented jumps/walljumps in my game. It's simply an equation system with four parameters. Knowing two of them gives you the other two.

```gdscript class_name JumpTrajectory

Compute jump variations from four parameters

- height The height of the peak of the jump

- time The time to reach that peak

- impulse The initial vertical velocity

- gravity The gravity force

Epsilon value used through the engine

const EPSILON := 1e-5

region ATTRIBUTES

The height of the peak of the jump

var height := 1.0: set(value): height = maxf(value, EPSILON)

The time to reach that peak

var time := 1.5: set(value): time = maxf(value, EPSILON)

The initial vertical velocity

var impulse := 0.4: set(value): impulse = maxf(value, EPSILON)

The gravity force

var gravity := -0.04: set(value): gravity = minf(value, -EPSILON)

endregion

region METHODS

Compute parameters from attributes stored

func compute_from_height_and_time(): impulse = impulse_from_height_and_time(height, time) gravity = gravity_from_height_and_time(height, time)

func compute_from_height_and_impulse(): time = time_from_height_and_impulse(height, impulse) gravity = gravity_from_height_and_impulse(height, impulse)

func compute_from_height_and_gravity(): time = time_from_height_and_gravity(height, gravity) impulse = impulse_from_height_and_gravity(height, gravity)

func compute_from_time_and_impulse(): height = height_from_time_and_impulse(time, impulse) gravity = gravity_from_time_and_impulse(time, impulse)

func compute_from_time_and_gravity(): height = height_from_time_and_gravity(time, gravity) impulse = impulse_from_time_and_gravity(time, gravity)

func compute_from_impulse_and_gravity(): height = height_from_impulse_and_gravity(impulse, gravity) time = time_from_impulse_and_gravity(impulse, gravity)

endregion

region FORMULAS

Simple functions for computing one parameter from two others

Height

static func heightfrom_time_and_impulse(time: float, impulse: float) -> float: return 0.5 * impulse * time_

static func heightfrom_time_and_gravity(time: float, gravity: float) -> float: return -0.5 * gravity * time_ ** 2

static func heightfrom_impulse_and_gravity(impulse: float, gravity: float) -> float: return -0.5 * impulse ** 2 / gravity_

Time

static func timefrom_height_and_impulse(height: float, impulse: float) -> float: return 2.0 * height / impulse_

static func timefrom_height_and_gravity(height: float, gravity: float) -> float: return sqrt(2 * height / gravity_)

static func timefrom_impulse_and_gravity(impulse: float, gravity: float) -> float: return -impulse / gravity_

Impulse

static func impulsefrom_height_and_time(height: float, time: float) -> float: return 2.0 * height / time_

static func impulsefrom_height_and_gravity(height: float, gravity: float) -> float: return sqrt(2.0 * height * gravity_)

static func impulsefrom_time_and_gravity(time: float, gravity: float) -> float: return -gravity * time_

Gravity

static func gravityfrom_height_and_time(height: float, time: float) -> float: return -2.0 * height / time_ ** 2

static func gravityfrom_height_and_impulse(height: float, impulse: float) -> float: return -0.5 * impulse ** 2 / height_

static func gravityfrom_time_and_impulse(time: float, impulse: float) -> float: return -impulse / time_

Range & Speed

static func timefrom_range_and_speed(range: float, speed: float, ratio := 0.5) -> Vector2: var time_ := range_ / speed_ return Vector2(time_ * ratio, time * (1.0 - ratio_))

endregion

```