Planar Envelopes

Planar envelopes are designed for lens-shaped mineralized bodies that can be represented on a single reference plane without self-overlap or internal holes. They are built from interval data and can be regenerated quickly when drilling information changes.

A planar envelope combines three elements:

• A reference plane
• A border prism (limits)
• The envelope mesh (top and bottom surfaces)

Create and Update

Create a planar envelope

From the context menu of mineralized intervals, choose Generate Planar Envelope.

At first creation, the Create Planar Properties dialog opens.

Update an existing planar envelope

Use one of these commands from the envelope context menu:

• Update Envelope: updates immediately with current settings.
• Update Envelope…: opens the properties dialog before updating.

Planar Properties Dialog

The dialog groups settings into envelope, prism, and constraints.

Prism Limits (Border)

The border prism defines the lateral footprint of the envelope on the reference plane.

Hull type

• Create a Convex Hull: creates a non-concave border.
• If unchecked, a concave border is generated.

Concavity controls

• Smoothing: controls how concave the border can be.
  • 0: most concave shape.
  • 1: equivalent to convex behavior.
• Concave Seed: changes the generated concave shape variant.

Margin controls

The “Margin” parameter is the radius of the circle (or half a segment of the cross). If the “Use Middle Distance” parameter is checked and the nearest borehole is at a distance less than the “Maximum Hole Distance”, the margin is calculated using the half of the distance between the hole and the end of the mineralized interval (double arrow of the following figure). Since normally you never want to exceed the margin, the “Maximum Hole Distance” should be half the margin. The interpretation to be given in this case is “I always apply the margin unless an empty hole is in the margin”. The margin is a maximum in this case. If the “Maximum Hole Distance” is greater than half of the margin, then the margin is a minimum in this case.

These settings define the distance between interval endpoints and the prism border:

• Margin: target offset around interval endpoints.
• Use Interval Enclosing Circle: builds the border using circular neighborhood points.
• Resolution: spacing used to densify perimeter points.
• Use Middle Distance: adapts local margin using nearby non-mineralized holes.
• Maximum Hole Distance: distance limit for middle-distance adaptation.

Practical guidance:

• To keep margin as an upper bound, set Maximum Hole Distance near half of Margin.
• Increase Resolution (finer spacing) if the border shape is not captured well.

Automatic vs manual prism

• In automatic mode, prism limits are regenerated during updates.
• You can switch to manual editing using Modify Limits on the prism.
• After manual conversion, returning to automatic regeneration requires recreating the planar envelope.
• You can also create a planar envelope directly from an existing prism using Create Planar Envelope.

Surface Generation

Surface generation settings control triangulation and border interpolation quality.

Minimal Distance

Minimal Distance controls whether very short intervals are treated as two distinct endpoints or effectively as a center point.

• Too small: can produce tiny triangles.
• Too large: can distort local interval honoring.

Border extrapolation behavior

Border points require estimated thickness and vertical positioning.

Key controls include:

• Thickness Exponent: controls how thickness is interpolated from nearby data.
• Order One / Order Two settings (weights and exponents): blend local smoothness and curvature response.
• Points Density: controls border densification after creation.

Practical guidance:

• Start with defaults.
• If border-following is poor, decrease Points Density to force denser boundary support.

Constraints

Constraints are used to guide or limit envelope geometry.

Interval line constraints

Use Set Interval Polylines to add control lines that behave like additional intervals and force surface passage.

Important:

• If the source polylines are changed later, reassign them to refresh envelope constraints.

Envelope thickness constraints

Use Set Envelope Thickness Constraints to prevent overlap with selected envelopes.

Main controls:

• Maximum Iterations: limits update passes.
• Envelopes Margin: enforces spacing between envelopes.

Recommended range for Maximum Iterations is typically low (for example, 2 to 10), balancing speed and precision.

You can convert computed thickness constraints into reusable lines with Create Constraint Intervals Polyline, then reuse them through Set Interval Polylines.

Envelope cutting constraints

Use Set Envelope Cutting Constraints to trim the planar envelope by selected envelope limits.

Use Prism Cutting Constraint when you want intersection-based cutting by a prism boundary.

Important:

• Cutting is applied to the central planar contour behavior, not as a full solid Boolean operation.
• Small local interpenetrations between upper/lower faces may remain in some cases.

Grade Estimation

Planar envelope grades are derived from triangulated support and nearby interval influence.

Main control:

• Grade Exponent: power used for inverse-distance estimation where direct support is missing.

Optional capping limits can be applied to reduce long-distance over-influence.

Special case:

• If Grade Exponent is set to 0, estimation switches to neighbor propagation across connected triangles.

Grade Estimation details

The triangulation used is that of Delaunay which happens to be the dual graph of the Voronoï diagrams well known in geology because they are used in the polygonal estimation method. All the points of a Voronoï cell have the fundamental property of being closer to the central point (here the central composite) than to any other composite. This property implies that for a given Delaunay triangle, its surface is generally divided into three major zones of influence, such that each point of this zone is closer to the composite than to any other composite (end of an interval for a planar envelope). Moreover, since the triangle is surrounded by the three zones of influence of its three composites, the influence of the other composites is thus negligible. You can see these properties in the following figure.

Therefore, if we consider that the grade of the triangular irregular prism is entirely determined by its three composites, it is possible to obtain an exact evaluation of the grade thereof. Indeed, we want that for the three composites A, B and C, the gradients of the amount of metal follow a linear distribution along the lines A-B, A-C and B-C. We know that this property is respected for the plan defined by points A, B, C and the amount of metal as elevation. It is thus possible to determine this plan for all properties: elevation, density and accumulation (metal content). It is therefore possible to create functions to determine these values at any point and thus integrate these functions on the entire surface of the triangle. If a point of a triangle does not have a composite because it is a point of the border or a control point, that value will be estimated by the method of the inverse of the distance to some power (“Grade Exponent” with the default at two). It is possible to add capping to indicate that from a certain distance, the value of the composite must be capped. For example, if a single composite contributes to the estimate of the point and is at a great distance, it would be wise to limit its value. It is possible to put up to three capping’s (A, B and C). In the case where the value of “Grade Exponent” would be zero, a simple propagation method is used. The value of a cell (triangle) is then determined by that of its neighbors weighted by their contact areas. The process is run until all cells are estimated.

Update Behavior Notes

During update, constraint lines are rebuilt and constraint envelopes are re-applied according to current settings.

When applicable, surface-based cutting constraints are also applied after the envelope update.

After a successful update, grade values are recalculated automatically.