page_title: Line moiré
section_title: The revealing lines inclination as a function of the superposition image’s lines inclination
hierarchical_section_title: Line moiré / Superposition of layers with inclined lines / The revealing lines inclination as a function of the superposition image’s lines inclination
caption_attribution_description: Line Moire - Figure 10. Inversed base layer and moiré lines
context_page_description: Line moiré is one type of moiré pattern; a pattern that appears when superposing two transparent layers containing correlated opaque patterns. Line moiré is the case when the superposed patterns comprise straight or curved lines. When moving the layer patterns, the moiré patterns transform or move at a faster speed. This effect is called optical moiré speedup.
context_section_description: Here is the equation for computing the revealing layer line inclination αᵣ for a given base layer line inclination αb, and a desired moiré line inclination αₘ:
  For any given base layer line inclination, this equation permits us to obtain a desired moiré line inclination by properly choosing the revealing layer inclination. In Figure 6 we showed an example where the curves of layers follow an identical inclination pattern forming a superposition image with the same inclination pattern. The inclination degrees of the layers’ and moiré lines change along the horizontal axis according to the following sequence of alternating degree values (+30, –30, +30, –30, +30). In Figure 9 we obtain the same superposition pattern as in Figure 6, but with a base layer comprising straight lines inclined by –10 degrees. The revealing pattern of Figure 9 is computed by interpolating the curves into connected straight lines, where for each position along the horizontal axis, the revealing line’s inclination angle αᵣ is computed as a function of αb and αₘ according to the equation above.
  Figure 9 demonstrates that the difference between the inclination angles of revealing and base layer lines has to be several times smaller than the difference between inclination angles of moiré and base layer lines.
  Another example forming the same superposition patterns as in Figure 6 and Figure 9 is shown in Figure 10. In Figure 10 the desired inclination pattern (+30, –30, +30, –30, +30) is obtained using a base layer with an inverted inclination pattern (–30, +30, –30, +30, –30).
  Figure 11 shows an animation where we obtain a superposition image with a constant inclination pattern of moiré lines (+30, –30, +30, –30, +30) for continuously modifying pairs of base and revealing layers. The base layer inclination pattern gradually changes and the revealing layer inclination pattern correspondingly adapts such that the superposition image’s inclination pattern remains the same.
caption: Figure 10. Inversed base layer and moiré lines
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