Dot Product-based Object Detection in Field of View: A Step-by-Step Tutorial

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dot product

The dot product can be used in detecting the "field of view" (FOV) in game development to determine whether an object or character is within the viewing range of another object or character. The FOV represents the angular range within which an entity can see or detect other entities.

Here's an example of how the dot product can be used for FOV detection:

  1. Setup:
    Let's consider a scenario where there is a player character with a fixed viewing direction or orientation represented by a normalized vector called "forward" (typically [0, 0, 1] in a 3D space, pointing along the positive z-axis). The player character also has a specified field of view angle, which represents the angular range within which it can see.
  2. Detection:
    For each object or character that needs to be checked for visibility within the player's FOV, we calculate the normalized vector from the player's position to the position of the target object. This vector is often referred to as the "toTarget" vector.
  3. Dot Product:
    Take the dot product of the "forward" vector and the "toTarget" vector. dotProduct = dot(forward, toTarget)
  4. Field of View Check:
    Compare the dot product value to a threshold based on the field of view angle. If the dot product is greater than or equal to the threshold, the target object is within the field of view of the player.

    threshold = cos(fovAngle / 2) (where fovAngle is the field of view angle in radians)
    If dotProduct >= threshold, the target object is visible within the FOV.
    If dotProduct < threshold, the target object is outside the FOV.

    The threshold value is obtained by taking the cosine of half the field of view angle. This accounts for the angle range from the center of the FOV in both directions.

    The dot product check in step 4 compares the alignment of the "forward" vector and the "toTarget" vector. If the vectors have a sufficiently small angle between them (i.e., the dot product is greater than or equal to the threshold), it indicates that the target object is within the field of view. Otherwise, if the angle is larger (i.e., the dot product is less than the threshold), the target object is outside the field of view.

    The dot product is calculated by taking the cosine of the angle between the vectors. By using the threshold value obtained from dividing the FOV angle by two, we ensure that the dot product exceeds the threshold when the object is within the desired angular range.
    In other words, dividing the FOV angle by two is a mathematical adjustment to obtain a threshold that aligns with the desired angular range from the center of the field of view. It allows for a direct comparison between the dot product and the threshold to determine if an object is within the field of view.

This technique can be used in game development for various purposes, such as determining if an enemy character is visible to the player character, detecting objects within a character's peripheral vision, or implementing AI behavior based on visibility and awareness.

Note that this is a simplified explanation, and in practice, additional considerations and optimizations may be required, such as taking into account the height of objects, occlusion, and visual obstructions, as well as performing checks within a limited range or cone-shaped FOV rather than a full 360-degree FOV.