Calculate Position That Camera Will See Object Unity

Calculating the position a camera will see an object in Unity involves understanding the camera's view frustum, projection matrices, and world-to-screen transformations. This guide explains the mathematical principles and provides a working calculator to determine the visible position of an object relative to the camera.

Introduction

In Unity, determining the position of an object as seen by a camera requires understanding the camera's view frustum and projection matrices. The process involves converting world coordinates to screen coordinates using the camera's transformation matrices.

The key steps include:

Getting the camera's view and projection matrices
Transforming the object's world position to view space
Applying the projection matrix to get clip space coordinates
Converting clip space coordinates to screen space

This calculation is essential for implementing features like object selection, UI positioning, and visibility checks in Unity applications.

Formula

The position of an object as seen by the camera can be calculated using the following steps:

Step 1: Get Camera Matrices

Retrieve the camera's view matrix (V) and projection matrix (P):

V = Camera.worldToCameraMatrix

P = Camera.projectionMatrix

Step 2: Transform to View Space

Convert the object's world position to view space:

viewPos = V × worldPos

Step 3: Apply Projection

Transform the view space position to clip space:

clipPos = P × viewPos

Step 4: Convert to Screen Space

Convert clip space coordinates to screen space:

screenX = (clipPos.x / clipPos.w + 1) × screenWidth / 2

screenY = (clipPos.y / clipPos.w + 1) × screenHeight / 2

Important Notes

The actual implementation in Unity may vary slightly depending on the camera's settings (orthographic/perspective) and the coordinate system being used. The above formulas represent the general approach.

Example Calculation

Let's calculate the screen position of an object at world coordinates (5, 3, 10) viewed by a camera with the following properties:

Camera position: (0, 0, 0)
Camera looking at: (0, 0, 1)
Screen resolution: 1920×1080
Field of view: 60 degrees

The exact calculation would involve Unity's built-in matrix operations, but the general approach would follow the steps outlined in the formula section.

Interpreting Results

The calculated screen position (x, y) represents where the object would appear on the camera's viewport. A negative x or y value indicates the object is outside the camera's view.

Key considerations:

Objects behind the camera (z < 0) will have negative z values in clip space
The screen coordinates are relative to the camera's viewport
For orthographic cameras, the z-coordinate doesn't affect the screen position

FAQ

How does Unity handle perspective vs orthographic cameras?

Perspective cameras use a projection matrix that accounts for depth, while orthographic cameras use a simpler matrix that maintains parallel lines. The calculation approach remains similar but the resulting screen positions differ.

What if the object is outside the camera's view?

The calculated screen position will be outside the camera's viewport (x or y values outside [0, screenWidth] or [0, screenHeight]). You can check if the object is visible by verifying the clip space z-coordinate is between -1 and 1.

How accurate is this calculation?

The calculation is mathematically accurate based on the camera's current matrices. However, Unity's rendering pipeline may apply additional transformations that aren't accounted for in this simplified formula.