If you’ve already picked out the three vertex indices of your triangle—say they are i1, i2, i3—and you have its outward unit normal n, then moving that face 2 units along the normal is as simple as:
function newVertices = translateTriangleAlongNormal(vertices, normal, amplitude)
% translateTriangleAlongNormal
% Translates a triangular face by a given amplitude along its normal vector.
%
% Args:
% vertices (double array): A 3x3 array where each row represents a vertex
% of the triangle (e.g., [x1, y1, z1; x2, y2, z2; x3, y3, z3]).
% normal (double array): A 1x3 array representing the face normal vector.
% amplitude (double): The distance to translate the face along the normal.
%
% Returns:
% double array: A 3x3 array with the new, translated vertex coordinates.
% Normalize the normal vector to ensure the translation is exactly `amplitude` units.
% The norm() function calculates the Euclidean length of the vector.
norm_length = norm(normal);
% Check for a zero-length normal to prevent division by zero.
if norm_length < 1e-6
disp("Warning: Normal vector has a magnitude of zero. Returning original vertices.");
newVertices = vertices;
return;
end
unitNormal = normal / norm_length;
% Calculate the translation vector by scaling the unit normal by the amplitude.
translationVector = unitNormal * amplitude;
% Apply the translation vector to each vertex of the triangle.
% The repmat() function is used to create a 3x3 matrix where each row is the
% translation vector, allowing for easy addition to the vertices matrix.
newVertices = vertices + repmat(translationVector, 3, 1);
end
% --- Main Example ---
% 1. Define the original triangular face vertices.
% Let's create a simple triangle on the XY-plane.
vertices = [0.0, 0.0, 0.0; % Vertex A
4.0, 0.0, 0.0; % Vertex B
2.0, 3.0, 0.0]; % Vertex C
% 2. Define the normal vector for this face.
% For a triangle on the XY-plane, the normal is pointing in the positive Z direction.
faceNormal = [0.0, 0.0, 1.0];
% 3. Define the translation amplitude.
amplitude = 2.0;
% 4. Perform the translation using our function.
translatedVertices = translateTriangleAlongNormal(vertices, faceNormal, amplitude);
% 5. Print the results to see the translation.
fprintf('Original Vertices:\n');
disp(vertices);
fprintf('\nFace Normal:\n');
disp(faceNormal);
fprintf('\nTranslation Amplitude: %f\n', amplitude);
fprintf('\nTranslated Vertices:\n');
disp(translatedVertices);
% Verification: The new Z-coordinates should be 2.
fprintf('\nVerification:\n');
fprintf('Original Z-coordinates: [%f, %f, %f]\n', vertices(:, 3));
fprintf('Translated Z-coordinates: [%f, %f, %f]\n', translatedVertices(:, 3));
