Calculator Input
Example Data Table
| Mode | Input example | Useful output | Graph command idea |
|---|---|---|---|
| Surface | z = sin(x)+cos(y), x and y from -5 to 5 | z range, gradient, tangent plane | Surface((u,v,sin(u)+cos(v)),u,-5,5,v,-5,5) |
| Plane | 2x - y + 3z - 6 = 0 | Normal vector and intercepts | 2x - y + 3z - 6 = 0 |
| Sphere | Center (1,-2,3), radius 4 | Area, volume, equation | Sphere((1,-2,3),4) |
| Curve | x=cos(t), y=sin(t), z=t/4 | Sample path and tangent vector | Curve(cos(t),sin(t),t/4,t,0,2*pi) |
| Vector | Start (0,0,0), end (3,4,5) | Magnitude, unit vector, angles | Vector((0,0,0),(3,4,5)) |
Formula Used
Surface: A surface is sampled from z = f(x,y). The gradient is estimated with central differences: fₓ ≈ [f(x+h,y)-f(x-h,y)] / 2h and fᵧ ≈ [f(x,y+h)-f(x,y-h)] / 2h.
Tangent plane: z = z₀ + fₓ(x-x₀) + fᵧ(y-y₀). This creates a local linear model at the chosen point.
Plane: Ax + By + Cz + D = 0. The normal vector is <A,B,C>. The origin distance is |D| / √(A²+B²+C²).
Sphere: (x-h)² + (y-k)² + (z-l)² = r². Area equals 4πr². Volume equals 4πr³/3.
Curve: r(t)=<x(t),y(t),z(t)>. Length is estimated by summing distances between sampled points. The tangent vector is estimated with central differences.
Vector: v = B - A. Magnitude is √(vₓ²+vᵧ²+v_z²). The unit vector is v / |v|.
How to Use This Calculator
- Select the graph mode that matches your 3D object.
- Enter expressions with explicit multiplication, such as 2*x.
- Use pi for π and functions like sin, cos, sqrt, log, and exp.
- Set domain ranges and sample counts for tables and exports.
- Press the calculate button to show results below the header.
- Copy the generated commands into a 3D graphing workspace.
- Download CSV for spreadsheet work or PDF for reports.
Advanced 3D Graphing Guide
Purpose
A 3D graphing calculator helps students and engineers test spatial ideas before drawing them by hand. This page focuses on graph preparation. It turns equations into sample data, commands, and supporting measurements. You can study a surface, plane, sphere, curve, or vector without changing pages.
Surface Analysis
Surface mode studies z as a function of x and y. The calculator samples a rectangular domain. It estimates the lowest value, highest value, average height, and local slope. The gradient shows the direction of fastest increase. The tangent plane gives a simple local model. This is useful in calculus, optimization, and engineering design.
Geometry Tools
Plane mode reads coefficients from the standard equation. It reports the normal vector, intercepts, and distance from the origin. Sphere mode builds the center-radius equation. It also gives area, volume, diameter, and edge points. Vector mode turns two points into a direction, magnitude, unit vector, and axis angles.
Curve Planning
Parametric curve mode accepts x(t), y(t), and z(t). It creates sample points along the interval. It estimates path length by adding short segment distances. It also estimates a tangent vector at the selected parameter. This helps when checking helices, paths, motion curves, or 3D sketches.
Workflow Benefits
The command output is designed for quick transfer into a graphing environment. The CSV file supports deeper checks in spreadsheets. The PDF file records the main result for lessons, assignments, or project notes. Use more samples for smoother tables. Use fewer samples for quick tests. Always check undefined points when expressions include roots, logs, or divisions.
FAQs
1. What expressions can I enter?
You can use numbers, variables, operators, parentheses, and common functions. Supported functions include sin, cos, tan, sqrt, log, log10, exp, abs, min, max, and pow.
2. Should I type 2x or 2*x?
Use 2*x. The calculator expects explicit multiplication. This avoids confusion between variables, functions, and constants during safe expression evaluation.
3. Can this make graph commands?
Yes. Each mode creates commands you can copy into a compatible 3D graphing workspace. Commands are also included in the PDF export.
4. Why do some sampled values show undefined?
A value becomes undefined when an expression fails at that point. Common causes include division by zero, square roots of negative values, or invalid logarithms.
5. How is the surface gradient calculated?
The calculator uses central differences near the chosen point. It evaluates the expression slightly before and after the point in both x and y directions.
6. What does sample count control?
Sample count controls how many points are generated. Larger values give richer tables but may take longer for complex expressions and wide domains.
7. Can I export my results?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a compact report with summary values and graph commands.
8. Is this only for surfaces?
No. It also supports planes, spheres, parametric curves, and vectors. This makes it useful for algebra, calculus, geometry, and physics tasks.