LinearCurve

Curve Visualization

%%{init: {"xychart": {"showTitle": true}} }%%

xychart-beta
    title "Linear Curve"
    x-axis "Assets (ETH)" [0.000000000000000000, 1.000000000000000000, 2.000000000000000000, 3.000000000000000000, 4.000000000000000000, 5.000000000000000000, 6.000000000000000000, 7.000000000000000000, 8.000000000000000000, 9.000000000000000000, 10.000000000000000000, 11.000000000000000000, 12.000000000000000000, 13.000000000000000000, 14.000000000000000000, 15.000000000000000000, 16.000000000000000000, 17.000000000000000000, 18.000000000000000000, 19.000000000000000000, 20.000000000000000000, 21.000000000000000000, 22.000000000000000000, 23.000000000000000000, 24.000000000000000000, 25.000000000000000000, 26.000000000000000000, 27.000000000000000000, 28.000000000000000000, 29.000000000000000000, 30.000000000000000000, 31.000000000000000000, 32.000000000000000000, 33.000000000000000000, 34.000000000000000000, 35.000000000000000000, 36.000000000000000000, 37.000000000000000000, 38.000000000000000000, 39.000000000000000000, 40.000000000000000000, 41.000000000000000000, 42.000000000000000000, 43.000000000000000000, 44.000000000000000000, 45.000000000000000000, 46.000000000000000000, 47.000000000000000000, 48.000000000000000000, 49.000000000000000000, 50.000000000000000000, 51.000000000000000000, 52.000000000000000000, 53.000000000000000000, 54.000000000000000000, 55.000000000000000000, 56.000000000000000000, 57.000000000000000000, 58.000000000000000000, 59.000000000000000000, 60.000000000000000000, 61.000000000000000000, 62.000000000000000000, 63.000000000000000000, 64.000000000000000000, 65.000000000000000000, 66.000000000000000000, 67.000000000000000000, 68.000000000000000000, 69.000000000000000000, 70.000000000000000000, 71.000000000000000000, 72.000000000000000000, 73.000000000000000000, 74.000000000000000000, 75.000000000000000000, 76.000000000000000000, 77.000000000000000000, 78.000000000000000000, 79.000000000000000000, 80.000000000000000000, 81.000000000000000000, 82.000000000000000000, 83.000000000000000000, 84.000000000000000000, 85.000000000000000000, 86.000000000000000000, 87.000000000000000000, 88.000000000000000000, 89.000000000000000000, 90.000000000000000000, 91.000000000000000000, 92.000000000000000000, 93.000000000000000000, 94.000000000000000000, 95.000000000000000000, 96.000000000000000000, 97.000000000000000000, 98.000000000000000000, 99.000000000000000000]
    y-axis "Shares"
    line [0.000000000000000000, 1.000000000000000000, 2.000000000000000000, 3.000000000000000000, 4.000000000000000000, 5.000000000000000000, 6.000000000000000000, 7.000000000000000000, 8.000000000000000000, 9.000000000000000000, 10.000000000000000000, 11.000000000000000000, 12.000000000000000000, 13.000000000000000000, 14.000000000000000000, 15.000000000000000000, 16.000000000000000000, 17.000000000000000000, 18.000000000000000000, 19.000000000000000000, 20.000000000000000000, 21.000000000000000000, 22.000000000000000000, 23.000000000000000000, 24.000000000000000000, 25.000000000000000000, 26.000000000000000000, 27.000000000000000000, 28.000000000000000000, 29.000000000000000000, 30.000000000000000000, 31.000000000000000000, 32.000000000000000000, 33.000000000000000000, 34.000000000000000000, 35.000000000000000000, 36.000000000000000000, 37.000000000000000000, 38.000000000000000000, 39.000000000000000000, 40.000000000000000000, 41.000000000000000000, 42.000000000000000000, 43.000000000000000000, 44.000000000000000000, 45.000000000000000000, 46.000000000000000000, 47.000000000000000000, 48.000000000000000000, 49.000000000000000000, 50.000000000000000000, 51.000000000000000000, 52.000000000000000000, 53.000000000000000000, 54.000000000000000000, 55.000000000000000000, 56.000000000000000000, 57.000000000000000000, 58.000000000000000000, 59.000000000000000000, 60.000000000000000000, 61.000000000000000000, 62.000000000000000000, 63.000000000000000000, 64.000000000000000000, 65.000000000000000000, 66.000000000000000000, 67.000000000000000000, 68.000000000000000000, 69.000000000000000000, 70.000000000000000000, 71.000000000000000000, 72.000000000000000000, 73.000000000000000000, 74.000000000000000000, 75.000000000000000000, 76.000000000000000000, 77.000000000000000000, 78.000000000000000000, 79.000000000000000000, 80.000000000000000000, 81.000000000000000000, 82.000000000000000000, 83.000000000000000000, 84.000000000000000000, 85.000000000000000000, 86.000000000000000000, 87.000000000000000000, 88.000000000000000000, 89.000000000000000000, 90.000000000000000000, 91.000000000000000000, 92.000000000000000000, 93.000000000000000000, 94.000000000000000000, 95.000000000000000000, 96.000000000000000000, 97.000000000000000000, 98.000000000000000000, 99.000000000000000000]

Inherits: BaseCurve

Author: 0xIntuition

A simple 1:1 price model implemented as a bonding curve. This curve maintains a direct linear relationship between assets and shares, where the conversion follows the formula: $$f(x) = x$$ where:

$x$ represents either assets or shares to be converted
$f(x)$ returns the corresponding amount in the target unit

The price mechanism relies on fee accumulation rather than supply-based pricing. As fees are collected, they are distributed proportionally across all shareholders, creating gradual appreciation in share value. This provides a conservative incentivization model where early participants benefit from fee accumulation over time.

This implementation offers a low-volatility approach to value accrual, suitable for scenarios where predictable, steady returns are preferred over dynamic pricing mechanisms.

This curve is not currently used in the EthMultiVault implementation to preserve audited code. It serves as a reference implementation demonstrating how traditional pro-rata share pricing can be adapted to the bonding curve architecture for future versions.

State Variables

MAX_SHARES

Maximum number of shares that can be handled by the curve.

uint256 public constant MAX_SHARES = type(uint256).max;

MAX_ASSETS

Maximum number of assets that can be handled by the curve.

uint256 public constant MAX_ASSETS = type(uint256).max;

Functions

constructor

Constructor for the Linear Curve.

constructor(string memory _name) BaseCurve(_name);

Parameters

Name	Type	Description
`_name`	`string`	The name of the curve.

previewDeposit

Computes the 1:1 relationship between assets <--> shares.

function previewDeposit(uint256 assets, uint256, uint256) external pure override returns (uint256);

Parameters

Name	Type	Description
`assets`	`uint256`	Quantity of assets to deposit
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`<none>`	`uint256`	shares The number of shares that would be minted

previewMint

Computes the 1:1 relationship between assets <--> shares.

function previewMint(uint256 shares, uint256, uint256) external pure override returns (uint256);

Parameters

Name	Type	Description
`shares`	`uint256`	Quantity of shares to mint
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`<none>`	`uint256`	assets The number of assets that would be required to mint the shares

previewWithdraw

Computes the 1:1 relationship between assets <--> shares.

function previewWithdraw(uint256 assets, uint256, uint256) external pure override returns (uint256);

Parameters

Name	Type	Description
`assets`	`uint256`	Quantity of assets to withdraw
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`<none>`	`uint256`	shares The number of shares that would need to be redeemed

previewRedeem

Computes the 1:1 relationship between assets <--> shares.

function previewRedeem(uint256 shares, uint256, uint256) external pure override returns (uint256);

Parameters

Name	Type	Description
`shares`	`uint256`	Quantity of shares to burn
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`<none>`	`uint256`	assets The number of assets that would be returned

convertToShares

Computes the 1:1 relationship between assets <--> shares.

function convertToShares(uint256 assets, uint256, uint256) external pure override returns (uint256 shares);

Parameters

Name	Type	Description
`assets`	`uint256`	Quantity of assets to convert to shares
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`shares`	`uint256`	The number of shares equivalent to the given assets

convertToAssets

Computes the 1:1 relationship between assets <--> shares.

function convertToAssets(uint256 shares, uint256, uint256) external pure override returns (uint256 assets);

Parameters

Name	Type	Description
`shares`	`uint256`	Quantity of shares to convert to assets
`<none>`	`uint256`
`<none>`	`uint256`

Returns

Name	Type	Description
`assets`	`uint256`	The number of assets equivalent to the given shares

currentPrice

In a linear curve, the base price will always be 1. Pool ratio adjustments are dealt with in the EthMultiVault itself.

function currentPrice(uint256) public pure override returns (uint256 sharePrice);

Parameters

Name	Type	Description
`<none>`	`uint256`

Returns

Name	Type	Description
`sharePrice`	`uint256`	The current price of a share, scaled by 1e18

maxShares

The maximum number of shares that this curve can handle without overflowing.

Checked by the EthMultiVault before transacting

function maxShares() external pure override returns (uint256);

maxAssets

The maximum number of assets that this curve can handle without overflowing.

Checked by the EthMultiVault before transacting

function maxAssets() external pure override returns (uint256);

Intuition Beta Contracts Documentation