Field Visualization Mapping

Let \(\mathbf{E}(\mathbf{x})\) be the electric field. We map it to pixel arrows as follows:

Brightness mode

• Arrow length is fixed: FIELD_FIXED_ARROW_LENGTH_PX.

• Alpha/brightness scales with magnitude: \(t = \mathrm{clamp}\big( s\,\|\mathbf{E}\| / L_{max} \big)\) where s = FIELD_BRIGHTNESS_SCALE, L_{max} = FIELD_VECTOR_MAX_LENGTH_PX.

• Color blends toward white as magnitude grows to enhance visibility.

Length mode

• Arrow length scales with magnitude: \(\ell = \mathrm{clamp}( \alpha \\|\mathbf{E}\\|, L_{max})\) with \alpha = FIELD_VECTOR_SCALE and clamp L_{max} = FIELD_VECTOR_MAX_LENGTH_PX.

Implementation: electrosim.rendering.field.draw_field_grid() and electrosim.rendering.field_sampler.ElectricFieldSampler.